Quantising proper actions on SpinC-manifolds
| dc.contributor.author | Hochs, P. | |
| dc.contributor.author | Mathai, V. | |
| dc.date.issued | 2017 | |
| dc.description.abstract | Paradan and Vergne generalised the quantisation commutes with reduction principle of Guillemin and Sternberg from symplectic to SpinC-manifolds. We extend their result to noncompact groups and manifolds. This leads to a result for cocompact actions, and a result for non-cocompact actions for reduction at zero. The result for cocompact actions is stated in terms of K-theory of group C*-algebras, and the result for non-cocompact actions is an equality of numerical indices. In the non-cocompact case, the result generalises to SpinC-Dirac operators twisted by vector bundles. This yields an index formula for Braverman's analytic index of such operators, in terms of characteristic classes on reduced spaces. | |
| dc.description.statementofresponsibility | Peter Hochs and Varghese Mathai | |
| dc.identifier.citation | The Asian Journal of Mathematics, 2017; 21(4):631-686 | |
| dc.identifier.doi | 10.4310/AJM.2017.v21.n4.a2 | |
| dc.identifier.issn | 1093-6106 | |
| dc.identifier.issn | 1945-0036 | |
| dc.identifier.orcid | Hochs, P. [0000-0001-9232-2936] | |
| dc.identifier.orcid | Mathai, V. [0000-0002-1100-3595] | |
| dc.identifier.uri | http://hdl.handle.net/2440/113188 | |
| dc.language.iso | en | |
| dc.publisher | International Press | |
| dc.rights | Copyright status unknown | |
| dc.source.uri | https://doi.org/10.4310/ajm.2017.v21.n4.a2 | |
| dc.subject | Geometric quantisation; quantisation commutes with reduction; proper Lie group actions; concompact index theorem | |
| dc.title | Quantising proper actions on SpinC-manifolds | |
| dc.type | Journal article | |
| pubs.publication-status | Published |