Matches in SemOpenAlex for { <https://semopenalex.org/work/W2953209008> ?p ?o ?g. }
- W2953209008 abstract "The Guillemin-Sternberg conjecture states that quantisation commutes with reduction in a specific technical setting. So far, this conjecture has almost exclusively been stated and proved for compact Lie groups $G$ acting on compact symplectic manifolds, and, largely due to the use of spin_c Dirac operator techniques, has reached a high degree of perfection under these compactness assumptions. In this paper we formulate an appropriate Guillemin-Sternberg conjecture in the general case, under the main assumptions that the Lie group action is proper and cocompact. This formulation is motivated by our interpretation of the quantisation commuates with reduction phenomenon as a special case of the functoriality of quantisation, and uses equivariant K-homology and the K-theory of the group C*-algebra C*(G) in a crucial way. For example, the equivariant index - which in the compact case takes values in the representation ring R(G) - is replaced by the analytic assembly map - which takes values in K_0(C*(G)) - familiar from the Baum-Connes conjecture in noncommutative geometry. Under the usual freeness assumption on the action, we prove our conjecture for all Lie groups G having a cocompact discrete normal subgroup, but we believe it is valid for all unimodular Lie groups." @default.
- W2953209008 created "2019-06-27" @default.
- W2953209008 creator A5049195995 @default.
- W2953209008 creator A5060266645 @default.
- W2953209008 date "2005-12-08" @default.
- W2953209008 modified "2023-09-28" @default.
- W2953209008 title "The Guillemin-Sternberg conjecture for noncompact groups and spaces" @default.
- W2953209008 cites W132667770 @default.
- W2953209008 cites W135327735 @default.
- W2953209008 cites W1495727713 @default.
- W2953209008 cites W1512909124 @default.
- W2953209008 cites W1514911332 @default.
- W2953209008 cites W1515192744 @default.
- W2953209008 cites W1529376890 @default.
- W2953209008 cites W1539551388 @default.
- W2953209008 cites W1552263642 @default.
- W2953209008 cites W1557857086 @default.
- W2953209008 cites W1580334901 @default.
- W2953209008 cites W1585078859 @default.
- W2953209008 cites W1586369843 @default.
- W2953209008 cites W1588860486 @default.
- W2953209008 cites W1595817164 @default.
- W2953209008 cites W1603569587 @default.
- W2953209008 cites W1676449817 @default.
- W2953209008 cites W1858572828 @default.
- W2953209008 cites W1924920156 @default.
- W2953209008 cites W1976254501 @default.
- W2953209008 cites W1978199434 @default.
- W2953209008 cites W1978654044 @default.
- W2953209008 cites W1989177327 @default.
- W2953209008 cites W1990028565 @default.
- W2953209008 cites W1991608737 @default.
- W2953209008 cites W2007579992 @default.
- W2953209008 cites W2012347126 @default.
- W2953209008 cites W2017808716 @default.
- W2953209008 cites W2023327993 @default.
- W2953209008 cites W2023686765 @default.
- W2953209008 cites W2025465045 @default.
- W2953209008 cites W2027628649 @default.
- W2953209008 cites W2028740420 @default.
- W2953209008 cites W2029422036 @default.
- W2953209008 cites W2041265694 @default.
- W2953209008 cites W2047062138 @default.
- W2953209008 cites W2053532032 @default.
- W2953209008 cites W2054842419 @default.
- W2953209008 cites W2065544517 @default.
- W2953209008 cites W2070560212 @default.
- W2953209008 cites W2086990318 @default.
- W2953209008 cites W2091209039 @default.
- W2953209008 cites W2091787559 @default.
- W2953209008 cites W2095635794 @default.
- W2953209008 cites W2095742649 @default.
- W2953209008 cites W2322345751 @default.
- W2953209008 cites W2951482851 @default.
- W2953209008 cites W3047929091 @default.
- W2953209008 cites W562933202 @default.
- W2953209008 cites W621245321 @default.
- W2953209008 doi "https://doi.org/10.48550/arxiv.math-ph/0512022" @default.
- W2953209008 hasPublicationYear "2005" @default.
- W2953209008 type Work @default.
- W2953209008 sameAs 2953209008 @default.
- W2953209008 citedByCount "2" @default.
- W2953209008 crossrefType "posted-content" @default.
- W2953209008 hasAuthorship W2953209008A5049195995 @default.
- W2953209008 hasAuthorship W2953209008A5060266645 @default.
- W2953209008 hasBestOaLocation W29532090081 @default.
- W2953209008 hasConcept C130133044 @default.
- W2953209008 hasConcept C136119220 @default.
- W2953209008 hasConcept C168619227 @default.
- W2953209008 hasConcept C171036898 @default.
- W2953209008 hasConcept C175322374 @default.
- W2953209008 hasConcept C18648836 @default.
- W2953209008 hasConcept C187915474 @default.
- W2953209008 hasConcept C201958917 @default.
- W2953209008 hasConcept C202444582 @default.
- W2953209008 hasConcept C22365015 @default.
- W2953209008 hasConcept C2780990831 @default.
- W2953209008 hasConcept C33923547 @default.
- W2953209008 hasConcept C40265840 @default.
- W2953209008 hasConcept C68797384 @default.
- W2953209008 hasConceptScore W2953209008C130133044 @default.
- W2953209008 hasConceptScore W2953209008C136119220 @default.
- W2953209008 hasConceptScore W2953209008C168619227 @default.
- W2953209008 hasConceptScore W2953209008C171036898 @default.
- W2953209008 hasConceptScore W2953209008C175322374 @default.
- W2953209008 hasConceptScore W2953209008C18648836 @default.
- W2953209008 hasConceptScore W2953209008C187915474 @default.
- W2953209008 hasConceptScore W2953209008C201958917 @default.
- W2953209008 hasConceptScore W2953209008C202444582 @default.
- W2953209008 hasConceptScore W2953209008C22365015 @default.
- W2953209008 hasConceptScore W2953209008C2780990831 @default.
- W2953209008 hasConceptScore W2953209008C33923547 @default.
- W2953209008 hasConceptScore W2953209008C40265840 @default.
- W2953209008 hasConceptScore W2953209008C68797384 @default.
- W2953209008 hasLocation W29532090081 @default.
- W2953209008 hasOpenAccess W2953209008 @default.
- W2953209008 hasPrimaryLocation W29532090081 @default.
- W2953209008 hasRelatedWork W1654999724 @default.
- W2953209008 hasRelatedWork W2019679678 @default.
- W2953209008 hasRelatedWork W2037235379 @default.