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Geometric methods in quantum theory.

Title
Geometric methods in quantum theory.
Funding
ARC | Discovery Projects
Contract (GA) number
DP0449470
Start Date
2004/01/01
End Date
2006/12/31
Open Access mandate
no
Organizations
-
More information
http://purl.org/au-research/grants/arc/DP0449470

 

  • On the relationship of gerbes to the odd families index theorem

    The goal of this paper is to apply the universal gerbe of \cite{CMi1} and \cite{CMi2} to give an alternative, simple and more unified view of the relationship between index theory and gerbes. We discuss determinant bundle gerbes \cite{CMMi1} and the index gerbe of \cite{L} for the case of families of Dirac operators on odd dimensional closed manifolds. The method also works for a family of Dirac operators on odd dimensional manifolds with boundary, for a pair of Melrose-Piazza's $Cl(1)$-spect...

    Thom isomorphism and Push-forward map in twisted K-theory

    We establish the Thom isomorphism in twisted K-theory for any real vector bundle and develop the push-forward map in twisted K-theory for any differentiable proper map $f: X\to Y$ (not necessarily K-oriented). The push-forward map generalizes the push-forward map in ordinary K-theory for any $K$-oriented differentiable proper map and the Atiyah-Singer index theorem of Dirac operators on Clifford modules. For $D$-branes satisfying Freed-Witten's anomaly cancellation condition in a manifold wit...
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