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POSITIVE SCALAR CURVATURE AND CALLIAS-TYPE INDEX THEOREMS FOR PROPER ACTIONS

Part of: Topological $K$-theory Partial differential equations on manifolds; differential operators Individual linear operators as elements of algebraic systems Infinite-dimensional manifolds $K$-theory and operator algebras

Published online by Cambridge University Press:  07 January 2019

HAO GUO Open the ORCID record for HAO GUO [Opens in a new window]
HAO GUO*
Affiliation:
School of Mathematical Sciences, University of Adelaide, Adelaide, South Australia 5005, Australia email oug.oah@gmail.com
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Abstract

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Keywords

positive scalar curvatureequivariant indexCallias operator

MSC classification

Primary: 58B34: Noncommutative geometry (à la Connes)
Secondary: 19K35: Kasparov theory ($KK$-theory) 19K56: Index theory 19L47: Equivariant $K$-theory 47C15: Operators in $C^*$- or von Neumann algebras 58J20: Index theory and related fixed point theorems
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 99 , Issue 2 , April 2019 , pp. 342 - 343
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

Footnotes

Thesis submitted to the University of Adelaide in July 2018; degree approved 8 August 2018; supervisors Mathai Varghese and Hang Wang.

References

Guo, H., ‘Index of equivariant Callias-type operators and invariant metrics of positive scalar curvature’. Preprint, 2018, arXiv:1803.05558.Google Scholar
Guo, H., Mathai, V. and Wang, H., ‘Positive scalar curvature and Poincaré duality for proper actions’. J. Noncommut. Geom., to appear. Preprint, 2016, arXiv:1609.01404.Google Scholar