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Title page for ETD etd-07252011-132556


Type of Document Dissertation
Author Wang, Hang
Author's Email Address hang.wang@vanderbilt.edu
URN etd-07252011-132556
Title L2-index formula for proper cocompact group actions
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Gennadi Kasparov Committee Chair
Guoliang Yu Committee Co-Chair
Bruce Hughes Committee Member
Kalman Varga Committee Member
Mark Sapir Committee Member
Keywords
  • proper action
  • L2-index
  • G-trace
Date of Defense 2011-05-13
Availability unrestricted
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.

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