{"id":"https://openalex.org/W7204921323","doi":"https://doi.org/10.48550/arxiv.2608.29524","title":"Kubo Formulas and Bulk-Edge Correspondence for Curved Boundaries","display_name":"Kubo Formulas and Bulk-Edge Correspondence for Curved Boundaries","publication_year":2026,"publication_date":"2026-08-30","ids":{"openalex":"https://openalex.org/W7204921323","doi":"https://doi.org/10.48550/arxiv.2608.29524"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.29524","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29524","pdf_url":"https://arxiv.org/pdf/2608.29524","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.29524","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022570325","display_name":"Aren Martinian","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Martinian, Aren","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5037134802","display_name":"Tom Stoiber","orcid":"https://orcid.org/0000-0002-5018-8430","observed_orcids":["https://orcid.org/0000-0002-5018-8430"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stoiber, Tom","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10657","display_name":"Topological Materials and Phenomena","score":0.9276999831199646,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10657","display_name":"Topological Materials and Phenomena","score":0.9276999831199646,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.06239999830722809,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.0012000000569969416,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/strong-topological-insulator","display_name":"strong topological insulator","score":0.8640000224113464},{"id":"https://openalex.org/keywords/bulk-boundary-correspondence","display_name":"bulk-boundary correspondence","score":0.8190000057220459},{"id":"https://openalex.org/keywords/curved-boundaries","display_name":"curved boundaries","score":0.8920000195503235},{"id":"https://openalex.org/keywords/kubo-formula","display_name":"Kubo formula","score":0.8259999752044678},{"id":"https://openalex.org/keywords/roe-algebras","display_name":"Roe algebras","score":0.9670000076293945},{"id":"https://openalex.org/keywords/kk-theory","display_name":"KK-theory","score":0.8939999938011169},{"id":"https://openalex.org/keywords/dirac-operator","display_name":"Dirac operator","score":0.777999997138977},{"id":"https://openalex.org/keywords/topological-degree","display_name":"topological degree","score":0.7720000147819519},{"id":"https://openalex.org/keywords/topological-invariants","display_name":"topological invariants","score":0.6370000243186951}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8069999814033508},{"id":"https://openalex.org/C14103023","wikidata":"https://www.wikidata.org/wiki/Q11681459","display_name":"Pairing","level":3,"score":0.6848000288009644},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.49399998784065247},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.49309998750686646},{"id":"https://openalex.org/C197617374","wikidata":"https://www.wikidata.org/wiki/Q755991","display_name":"Atiyah\u2013Singer index theorem","level":2,"score":0.40149998664855957},{"id":"https://openalex.org/C2779219991","wikidata":"https://www.wikidata.org/wiki/Q573631","display_name":"Fredholm operator","level":4,"score":0.37290000915527344},{"id":"https://openalex.org/C2779832538","wikidata":"https://www.wikidata.org/wiki/Q2308809","display_name":"Coincidence","level":3,"score":0.37209999561309814},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.3702999949455261},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.3601999878883362},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.35839998722076416},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.3488999903202057},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.3248000144958496},{"id":"https://openalex.org/C2777044963","wikidata":"https://www.wikidata.org/wiki/Q5384707","display_name":"Equivalence class (music)","level":2,"score":0.30000001192092896},{"id":"https://openalex.org/C158650840","wikidata":"https://www.wikidata.org/wiki/Q907439","display_name":"Dirac operator","level":2,"score":0.29820001125335693},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29339998960494995},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.2669999897480011},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26170000433921814},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.258899986743927},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.25769999623298645},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.25609999895095825}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.29524","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29524","pdf_url":"https://arxiv.org/pdf/2608.29524","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.29524","doi":"https://doi.org/10.48550/arxiv.2608.29524","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.29524","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.29524","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29524","pdf_url":"https://arxiv.org/pdf/2608.29524","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1450200979","display_name":"Spectral Transitions and Critical Phenomena","funder_award_id":"2155211","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6852334964","display_name":"Graduate Research Fellowship Program (GRFP)","funder_award_id":"2146752","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7023593522","display_name":"FRG: Collaborative Research: Non-Perturbative Analysis for Multi-Dimensional Quasiperiodic Systems","funder_award_id":"2052899","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204921323.pdf","grobid_xml":"https://content.openalex.org/works/W7204921323.grobid-xml"},"referenced_works_count":53,"referenced_works":["https://openalex.org/W120675131","https://openalex.org/W562933202","https://openalex.org/W649789958","https://openalex.org/W1507062495","https://openalex.org/W1528946541","https://openalex.org/W1530217273","https://openalex.org/W1581464763","https://openalex.org/W1827381112","https://openalex.org/W1928023118","https://openalex.org/W1966642002","https://openalex.org/W1987914519","https://openalex.org/W1989661400","https://openalex.org/W2001397204","https://openalex.org/W2011756913","https://openalex.org/W2016164707","https://openalex.org/W2037807652","https://openalex.org/W2038652661","https://openalex.org/W2047755298","https://openalex.org/W2055829282","https://openalex.org/W2058531556","https://openalex.org/W2065392201","https://openalex.org/W2083022424","https://openalex.org/W2116020431","https://openalex.org/W2141708961","https://openalex.org/W2460349219","https://openalex.org/W2775545383","https://openalex.org/W2787002775","https://openalex.org/W2787172562","https://openalex.org/W2884427691","https://openalex.org/W2888201481","https://openalex.org/W2921974725","https://openalex.org/W2952176028","https://openalex.org/W2963489567","https://openalex.org/W2974222813","https://openalex.org/W3001445364","https://openalex.org/W3112537439","https://openalex.org/W3124802064","https://openalex.org/W3161599517","https://openalex.org/W3205747093","https://openalex.org/W4248744331","https://openalex.org/W4313901789","https://openalex.org/W4365601161","https://openalex.org/W4388571268","https://openalex.org/W4392627822","https://openalex.org/W4406022808","https://openalex.org/W4410192393","https://openalex.org/W4411932271","https://openalex.org/W4413866693","https://openalex.org/W4414816009","https://openalex.org/W4416282447","https://openalex.org/W6910344161","https://openalex.org/W7128359410","https://openalex.org/W7166163391"],"related_works":["https://openalex.org/W7211913082","https://openalex.org/W2559257910","https://openalex.org/W4400846025","https://openalex.org/W7081578686","https://openalex.org/W4403671367","https://openalex.org/W2241901448","https://openalex.org/W2038722631","https://openalex.org/W7166163391","https://openalex.org/W2765175976","https://openalex.org/W4293360154"],"abstract_inverted_index":{"Strong":[0],"topological":[1,113],"insulators":[2],"are":[3,95],"classified":[4],"by":[5,14,133],"integer":[6],"invariants":[7,19],"which":[8,127],"admit":[9],"different":[10],"real-space":[11,135],"expressions.":[12],"Inspired":[13],"recent":[15],"work":[16],"studying":[17],"these":[18,93],"for":[20,54,65],"spaces":[21,82],"with":[22,69,100,106],"curved":[23],"boundaries,":[24],"we":[25,57,87,121],"revisit":[26],"the":[27,32,66,76,101,107,112,116,129],"problem":[28],"of":[29,31,51,62,78,115],"equivalence":[30],"various":[33],"expressions,":[34],"including":[35],"Fredholm":[36],"index":[37,67,131],"pairings":[38,94],"and":[39,48],"Kubo":[40,125],"formulas":[41],"involving":[42],"half-space":[43],"projections.":[44],"Using":[45],"Roe":[46],"algebras":[47],"a":[49,59,70,123,134],"variant":[50],"KK-theory":[52],"suitable":[53],"non-separable":[55],"$C^*$-algebras,":[56],"prove":[58,122],"general":[60,71,130],"form":[61],"bulk-edge":[63],"correspondence":[64],"pairing":[68,132],"position-space":[72],"Dirac":[73,104],"operator":[74],"in":[75],"presence":[77],"arbitrary":[79],"boundaries.":[80],"For":[81],"coarsely":[83],"equivalent":[84],"to":[85,91,97],"$\\mathbb{R}^d$,":[86],"show":[88],"that":[89],"up":[90],"multiplicity,":[92],"equal":[96],"those":[98],"obtained":[99],"standard":[102],"dual":[103],"operator,":[105],"multiplicity":[108],"explicitly":[109],"given":[110],"as":[111],"degree":[114],"symbol":[117],"function.":[118],"In":[119],"addition,":[120],"generalized":[124],"formula":[126],"computes":[128],"formula.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}
