{"id":"https://openalex.org/W7213278338","doi":"https://doi.org/10.48550/arxiv.2609.14369","title":"Morse Index of a $G_2$-Instanton over $S^7$","display_name":"Morse Index of a $G_2$-Instanton over $S^7$","publication_year":2026,"publication_date":"2026-09-13","ids":{"openalex":"https://openalex.org/W7213278338","doi":"https://doi.org/10.48550/arxiv.2609.14369"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.14369","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14369","pdf_url":"https://arxiv.org/pdf/2609.14369","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/2609.14369","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151748170","display_name":"Xiaoli Han","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Han, Xiaoli","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5151851211","display_name":"Yang Wen","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wen, Yang","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":0,"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/T12351","display_name":"Geometry and complex manifolds","score":0.9032999873161316,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12351","display_name":"Geometry and complex manifolds","score":0.9032999873161316,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.05139999836683273,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.016200000420212746,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/morse-index","display_name":"Morse index","score":0.8809999823570251},{"id":"https://openalex.org/keywords/g2-instantons","display_name":"G2-instantons","score":0.8849999904632568},{"id":"https://openalex.org/keywords/s-7","display_name":"S^7","score":0.6320000290870667},{"id":"https://openalex.org/keywords/yang-mills-connections","display_name":"Yang-Mills connections","score":0.8460000157356262},{"id":"https://openalex.org/keywords/jacobi-operator","display_name":"Jacobi operator","score":0.9660000205039978},{"id":"https://openalex.org/keywords/coulomb-gauge","display_name":"Coulomb gauge","score":0.9440000057220459},{"id":"https://openalex.org/keywords/zero-modes","display_name":"zero modes","score":0.7820000052452087},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.3440000116825104},{"id":"https://openalex.org/keywords/deformation-space","display_name":"deformation space","score":0.5139999985694885}],"concepts":[{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.7878000140190125},{"id":"https://openalex.org/C140031139","wikidata":"https://www.wikidata.org/wiki/Q79897","display_name":"Morse code","level":2,"score":0.7660999894142151},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7616000175476074},{"id":"https://openalex.org/C54486226","wikidata":"https://www.wikidata.org/wiki/Q493941","display_name":"Fibration","level":3,"score":0.4999000132083893},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.49939998984336853},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.49070000648498535},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4758000075817108},{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.462799996137619},{"id":"https://openalex.org/C156730297","wikidata":"https://www.wikidata.org/wiki/Q2296951","display_name":"Morse theory","level":2,"score":0.435699999332428},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4124999940395355},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.41019999980926514},{"id":"https://openalex.org/C55232844","wikidata":"https://www.wikidata.org/wiki/Q1627604","display_name":"Hopf fibration","level":2,"score":0.3968999981880188},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.3716000020503998},{"id":"https://openalex.org/C24296071","wikidata":"https://www.wikidata.org/wiki/Q5121372","display_name":"Circle-valued Morse theory","level":3,"score":0.3630000054836273},{"id":"https://openalex.org/C7979169","wikidata":"https://www.wikidata.org/wiki/Q1142143","display_name":"Cotangent bundle","level":3,"score":0.34049999713897705},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.337799996137619},{"id":"https://openalex.org/C136005978","wikidata":"https://www.wikidata.org/wiki/Q1362077","display_name":"First variation","level":2,"score":0.3230000138282776},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.30309998989105225},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.2928999960422516},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.2806999981403351},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.2768999934196472},{"id":"https://openalex.org/C2777680557","wikidata":"https://www.wikidata.org/wiki/Q7259417","display_name":"Pullback","level":2,"score":0.27219998836517334},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.2705000042915344},{"id":"https://openalex.org/C204366326","wikidata":"https://www.wikidata.org/wiki/Q3027650","display_name":"Deformation (meteorology)","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25929999351501465},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.2535000145435333}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.14369","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14369","pdf_url":"https://arxiv.org/pdf/2609.14369","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.2609.14369","doi":"https://doi.org/10.48550/arxiv.2609.14369","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.14369","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:2609.14369","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14369","pdf_url":"https://arxiv.org/pdf/2609.14369","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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213278338.pdf","grobid_xml":"https://content.openalex.org/works/W7213278338.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4400738519","https://openalex.org/W1568525986","https://openalex.org/W7096895081","https://openalex.org/W3004704251","https://openalex.org/W2954067996","https://openalex.org/W3099869714","https://openalex.org/W2469184401","https://openalex.org/W2793706742","https://openalex.org/W2286974345","https://openalex.org/W4294440095"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"determine":[4],"the":[5,9,17,25,35,41,44,49,65,68,78,95],"nonpositive":[6],"spectrum":[7],"of":[8,52,64,67],"Yang-Mills":[10,54],"Jacobi":[11,69],"operator":[12],"in":[13],"Coulomb":[14],"gauge":[15],"at":[16],"standard":[18],"$G_2$-instanton":[19],"on":[20,56],"$S^7$.":[21,57],"We":[22,58],"prove":[23],"that":[24,91],"only":[26],"negative":[27],"eigenvalue":[28],"is":[29],"$-3$,":[30],"with":[31],"multiplicity":[32],"$8$,":[33],"and":[34],"kernel":[36],"has":[37],"dimension":[38],"$20$.":[39],"Thus":[40],"connection":[42],"attains":[43],"sharp":[45],"lower":[46],"bound":[47],"for":[48,77],"Morse":[50],"index":[51],"nonflat":[53],"connections":[55],"also":[59],"give":[60],"an":[61],"explicit":[62],"description":[63],"kernal":[66],"operator,":[70],"which":[71],"contains":[72],"Waldron's":[73],"$15$-dimensional":[74],"deformation":[75],"space":[76],"fixed":[79],"nearly":[80],"parallel":[81],"$G_2$-structure.":[82],"The":[83],"5":[84],"additional":[85],"zero":[86],"modes":[87],"are":[88],"isometry-induced":[89],"variations":[90],"do":[92],"not":[93],"satisfy":[94],"corresponding":[96],"linearized":[97],"instanton":[98],"equation.":[99]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-16T00:00:00"}
