{"id":"https://openalex.org/W7214328985","doi":"https://doi.org/10.48550/arxiv.2609.28907","title":"On symplectic aspects of $SU(2)$ character varieties for punctured surfaces","display_name":"On symplectic aspects of $SU(2)$ character varieties for punctured surfaces","publication_year":2026,"publication_date":"2026-09-24","ids":{"openalex":"https://openalex.org/W7214328985","doi":"https://doi.org/10.48550/arxiv.2609.28907"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.28907","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28907","pdf_url":"https://arxiv.org/pdf/2609.28907","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/2609.28907","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010788056","display_name":"Aliakbar Daemi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daemi, Aliakbar","raw_affiliation_strings":["Aliakbar Daemi , DEPARTMENT OF MATHEMATICS , WASHINGTON UNIVERSITY IN ST. LOUIS , ONE BROOKINGS DRIVE , ROOM 212 , ST. LOUIS , MO 63130"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Aliakbar Daemi , DEPARTMENT OF MATHEMATICS , WASHINGTON UNIVERSITY IN ST. LOUIS , ONE BROOKINGS DRIVE , ROOM 212 , ST. LOUIS , MO 63130","institution_ids":["https://openalex.org/I204465549"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023767613","display_name":"Christopher W. Scaduto","orcid":"https://orcid.org/0000-0002-3641-8586","observed_orcids":["https://orcid.org/0000-0002-3641-8586"]},"institutions":[{"id":"https://openalex.org/I145608581","display_name":"University of Miami","ror":"https://ror.org/02dgjyy92","country_code":"US","type":"education","lineage":["https://openalex.org/I145608581"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Scaduto, Christopher","raw_affiliation_strings":["DEPARTMENT OF MATHEMATICS , UNIVERSITY OF MIAMI , 1365 MEMORIAL DR 515 , CORAL GABLES , FL 33124"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DEPARTMENT OF MATHEMATICS , UNIVERSITY OF MIAMI , 1365 MEMORIAL DR 515 , CORAL GABLES , FL 33124","institution_ids":["https://openalex.org/I145608581"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9990000128746033,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9990000128746033,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.0003000000142492354,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.00019999999494757503,"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/punctured-surfaces","display_name":"punctured surfaces","score":0.9079999923706055},{"id":"https://openalex.org/keywords/flat-connections","display_name":"flat connections","score":0.734000027179718},{"id":"https://openalex.org/keywords/lagrangian-spheres","display_name":"Lagrangian spheres","score":0.7879999876022339},{"id":"https://openalex.org/keywords/heegaard-splittings","display_name":"Heegaard splittings","score":0.8709999918937683},{"id":"https://openalex.org/keywords/hamiltonian-isotopy","display_name":"Hamiltonian isotopy","score":0.6880000233650208}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7802000045776367},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.7638999819755554},{"id":"https://openalex.org/C73373263","wikidata":"https://www.wikidata.org/wiki/Q845677","display_name":"Moduli space","level":2,"score":0.7457000017166138},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5911999940872192},{"id":"https://openalex.org/C2778876713","wikidata":"https://www.wikidata.org/wiki/Q1361125","display_name":"Isotopy","level":2,"score":0.5458999872207642},{"id":"https://openalex.org/C196278274","wikidata":"https://www.wikidata.org/wiki/Q3845212","display_name":"Mapping class group","level":3,"score":0.4830999970436096},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.40290001034736633},{"id":"https://openalex.org/C3387666","wikidata":"https://www.wikidata.org/wiki/Q6889798","display_name":"Moduli of algebraic curves","level":3,"score":0.40059998631477356},{"id":"https://openalex.org/C39290043","wikidata":"https://www.wikidata.org/wiki/Q1475760","display_name":"Projective plane","level":3,"score":0.3961000144481659},{"id":"https://openalex.org/C32518243","wikidata":"https://www.wikidata.org/wiki/Q907926","display_name":"Holonomy","level":2,"score":0.38280001282691956},{"id":"https://openalex.org/C121294916","wikidata":"https://www.wikidata.org/wiki/Q652525","display_name":"Floer homology","level":3,"score":0.3813000023365021},{"id":"https://openalex.org/C130190758","wikidata":"https://www.wikidata.org/wiki/Q1064500","display_name":"Symplectic manifold","level":3,"score":0.3675000071525574},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3562999963760376},{"id":"https://openalex.org/C135661100","wikidata":"https://www.wikidata.org/wiki/Q1049064","display_name":"Symplectomorphism","level":3,"score":0.30730000138282776},{"id":"https://openalex.org/C197375991","wikidata":"https://www.wikidata.org/wiki/Q1464936","display_name":"Poisson manifold","level":3,"score":0.305400013923645},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.29580000042915344},{"id":"https://openalex.org/C75280867","wikidata":"https://www.wikidata.org/wiki/Q877775","display_name":"Projective space","level":3,"score":0.29330000281333923},{"id":"https://openalex.org/C77462122","wikidata":"https://www.wikidata.org/wiki/Q15176852","display_name":"Intersection theory","level":5,"score":0.28690001368522644},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.2809000015258789},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C125198404","wikidata":"https://www.wikidata.org/wiki/Q1192916","display_name":"Instanton","level":2,"score":0.27880001068115234},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.2766000032424927},{"id":"https://openalex.org/C125849494","wikidata":"https://www.wikidata.org/wiki/Q766774","display_name":"Symplectic vector space","level":5,"score":0.27630001306533813},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C90738871","wikidata":"https://www.wikidata.org/wiki/Q41642869","display_name":"Configuration space","level":2,"score":0.26170000433921814},{"id":"https://openalex.org/C175322374","wikidata":"https://www.wikidata.org/wiki/Q936434","display_name":"Symplectic group","level":3,"score":0.26030001044273376},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.2547999918460846},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.25450000166893005}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.28907","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28907","pdf_url":"https://arxiv.org/pdf/2609.28907","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.2609.28907","doi":"https://doi.org/10.48550/arxiv.2609.28907","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.28907","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.28907","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28907","pdf_url":"https://arxiv.org/pdf/2609.28907","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214328985.pdf","grobid_xml":"https://content.openalex.org/works/W7214328985.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W4391940754","https://openalex.org/W4394668678","https://openalex.org/W4403789113","https://openalex.org/W7108643190"],"related_works":["https://openalex.org/W2767822751","https://openalex.org/W2963355847","https://openalex.org/W2077922500","https://openalex.org/W3129168216","https://openalex.org/W3103958168","https://openalex.org/W2021749385","https://openalex.org/W1968908719","https://openalex.org/W2941713919","https://openalex.org/W2075597894","https://openalex.org/W7095110102"],"abstract_inverted_index":{"For":[0],"a":[1,23,34,88,130],"surface":[2,45],"with":[3,16,103],"an":[4],"odd":[5],"number":[6],"of":[7,12,42,52,70,81,91,143,166,170],"punctures,":[8],"the":[9,27,38,43,47,68,71,95,110,114,141,164,171],"moduli":[10,28,54,72,111,173],"space":[11,29,73,112,174],"flat":[13],"$SU(2)$":[14,172],"connections":[15],"traceless":[17],"holonomy":[18,176],"around":[19],"each":[20],"puncture":[21],"is":[22,30,33,57,62,74,87,109,119],"symplectic":[24,48,106,131],"manifold.":[25],"When":[26],"nonempty,":[31],"there":[32],"natural":[35],"homomorphism":[36,61],"from":[37],"mapping":[39,49],"class":[40,50],"group":[41,51],"punctured":[44],"to":[46],"this":[53,60],"space.":[55],"It":[56],"shown":[58],"that":[59],"injective":[63],"if":[64,67],"and":[65,83,154],"only":[66],"dimension":[69],"greater":[75],"than":[76],"$2$.":[77],"This":[78],"generalizes":[79],"work":[80],"Seidel":[82],"Wehrheim--Woodward.":[84],"Also":[85],"given":[86],"complete":[89],"classification":[90],"Lagrangian":[92,124,138],"spheres":[93,125,139],"in":[94,140,146,181],"projective":[96],"plane":[97],"blown":[98],"up":[99],"at":[100],"$5$":[101],"points":[102],"its":[104],"monotone":[105],"structure,":[107],"which":[108,178],"for":[113],"5-punctured":[115],"sphere.":[116],"Furthermore,":[117],"it":[118],"determined":[120],"when":[121],"two":[122,144],"such":[123],"can":[126],"be":[127],"displaced":[128],"by":[129,175],"isotopy.":[132],"Results":[133],"are":[134,179],"also":[135],"obtained":[136],"regarding":[137],"intersection":[142],"quadrics":[145],"$\\mathbb{C}\\mathbb{P}^5$.":[147],"The":[148],"proofs":[149],"involve":[150],"instanton":[151,182],"Floer":[152],"theory":[153],"results":[155],"on":[156],"Heegaard":[157],"splittings.":[158],"A":[159],"main":[160],"technical":[161],"result":[162],"establishes":[163],"approximation":[165],"any":[167],"Hamiltonian":[168],"isotopy":[169],"perturbations":[177],"used":[180],"homology.":[183]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-26T00:00:00"}