scholarly journals The chiral index of the fermionic signature operator

2017 ◽  
Vol 24 (1) ◽  
pp. 37-66
Author(s):  
Felix Finster
Keyword(s):  
Signature Operator

scholarly journals The fermionic signature operator in de Sitter spacetime

2020 ◽  
Vol 485 (2) ◽  
pp. 123808 ◽  
Author(s):  
Claudio Dappiaggi ◽  
Felix Finster ◽  
Simone Murro ◽  
Emanuela Radici
Keyword(s):  
De Sitter Spacetime ◽  
De Sitter ◽  
Signature Operator ◽  
Sitter Spacetime

scholarly journals CIRCLE ACTION AND SOME VANISHING RESULTS ON MANIFOLDS

2011 ◽  
Vol 22 (11) ◽  
pp. 1603-1610 ◽  
Author(s):  
PING LI ◽  
KEFENG LIU
Keyword(s):  
Fixed Point ◽  
Rigidity Theorem ◽  
Circle Action ◽  
Dimensional Manifold ◽  
Fixed Point Set ◽  
Circle Actions ◽  
Signature Operator ◽  
Spin Manifolds ◽  
Point Set

Kawakubo and Uchida showed that, if a closed oriented 4k-dimensional manifold M admits a semi-free circle action such that the dimension of the fixed point set is less than 2k, then the signature of M vanishes. In this note, by using G-signature theorem and the rigidity of the signature operator, we generalize this result to more general circle actions. Combining the same idea with the remarkable Witten–Taubes–Bott rigidity theorem, we explore more vanishing results on spin manifolds admitting such circle actions. Our results are closely related to some earlier results of Conner–Floyd, Landweber–Stong and Hirzebruch–Slodowy.

scholarly journals The fermionic signature operator and space-time symmetries

2018 ◽  
Vol 22 (8) ◽  
pp. 1907-1937
Author(s):  
Felix Finster ◽  
Moritz Reintjes
Keyword(s):  
Space Time ◽  
Signature Operator

scholarly journals SPECTRAL FLOW, INDEX AND THE SIGNATURE OPERATOR

2011 ◽  
Vol 03 (01) ◽  
pp. 37-67 ◽  
Author(s):  
SARA AZZALI ◽  
CHARLOTTE WAHL
Keyword(s):  
Von Neumann Algebra ◽  
Flow Index ◽  
Spectral Flow ◽  
Bounded Operators ◽  
Fredholm Operators ◽  
Foliated Manifold ◽  
Von Neumann ◽  
Signature Operator ◽  
Integral Formulas ◽  
Manifold With Boundary

We relate the spectral flow to the index for paths of selfadjoint Breuer–Fredholm operators affiliated to a semifinite von Neumann algebra, generalizing results of Robbin–Salamon and Pushnitski. Then we prove the vanishing of the von Neumann spectral flow for the tangential signature operator of a foliated manifold when the metric is varied. We conclude that the tangential signature of a foliated manifold with boundary does not depend on the metric. In the Appendix we reconsider integral formulas for the spectral flow of paths of bounded operators.

scholarly journals The signature operator at 2

Topology ◽  
2006 ◽  
Vol 45 (1) ◽  
pp. 47-63 ◽  
Author(s):  
Jonathan Rosenberg ◽  
Shmuel Weinberger
Keyword(s):  
Signature Operator

scholarly journals Mapping the surgery exact sequence for topological manifolds to analysis

2017 ◽  
Vol 09 (02) ◽  
pp. 329-361 ◽  
Author(s):  
Vito Felice Zenobi
Keyword(s):  
Exact Sequence ◽  
Dirac Operator ◽  
Index Theorem ◽  
Fundamental Result ◽  
Natural Mapping ◽  
Signature Operator ◽  
Surgery Exact Sequence ◽  
Topological Manifolds ◽  
Stability Results ◽  
Odd Dimensions

In this paper we prove the existence of a natural mapping from the surgery exact sequence for topological manifolds to the analytic surgery exact sequence of Higson and Roe. This generalizes the fundamental result of Higson and Roe, but in the treatment given by Piazza and Schick, from smooth manifolds to topological manifolds. Crucial to our treatment is the Lipschitz signature operator of Teleman. We also give a generalization to the equivariant setting of the product defined by Siegel in his Ph.D. thesis. Geometric applications are given to stability results for rho classes. We also obtain a proof of the APS delocalized index theorem on odd dimensional manifolds, both for the spin Dirac operator and the signature operator, thus extending to odd dimensions the results of Piazza and Schick. Consequently, we are able to discuss the mapping of the surgery sequence in all dimensions.

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