dc.creator | Wang, Hang | |
dc.date.accessioned | 2020-08-22T20:35:05Z | |
dc.date.available | 2012-02-11 | |
dc.date.issued | 2011-08-15 | |
dc.identifier.uri | https://etd.library.vanderbilt.edu/etd-07252011-132556 | |
dc.identifier.uri | http://hdl.handle.net/1803/13579 | |
dc.description.abstract | Indices are analytical invariants to some elliptic operators and an index formula provides a way to interpret the analysis quantity using the topological invariants.
The thesis computes the L2-index of a properly supported elliptic pseudo-differential operator which acts on a complete Riemannian manifold and being invariant under a properly cocompact group action.
The group is assumed to be a locally compact one admitting an invariant Haar measure.
The L2-index of an invariant elliptic operator is defined by taking the von Neumann trace of the higher index in the K-theory of the group C*-algebra. The thesis provides a cohomological formula for the L2-index for elliptic operators with properly cocompact group actions using the KK-theory and the heat kernel method. The formula is a generalization to the Atiyah's L2-index theorem for free cocompact group actions and to the Connes and Moscovici's L2-index formula for homogenous space of unimodular Lie group. | |
dc.format.mimetype | application/pdf | |
dc.subject | proper action | |
dc.subject | L2-index | |
dc.subject | G-trace | |
dc.title | L2-index formula for proper cocompact group actions | |
dc.type | dissertation | |
dc.contributor.committeeMember | Mark Sapir | |
dc.contributor.committeeMember | Kalman Varga | |
dc.contributor.committeeMember | Bruce Hughes | |
dc.type.material | text | |
thesis.degree.name | PHD | |
thesis.degree.level | dissertation | |
thesis.degree.discipline | Mathematics | |
thesis.degree.grantor | Vanderbilt University | |
local.embargo.terms | 2012-02-11 | |
local.embargo.lift | 2012-02-11 | |
dc.contributor.committeeChair | Gennadi Kasparov | |
dc.contributor.committeeChair | Guoliang Yu | |