ISSN:
1573-0514
Keywords:
Lipschitz manifold
;
Teleman signature operator
;
G-signature theorem
;
Novikov Conjecture
;
equivariantK-theory
;
KK-theory
;
nonlinear similarity
;
Atiyah-Bott number
;
surgery
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Using the Teleman signature operator and Kasparov'sKK-theory, we prove a strong De Rham theorem and a higherG-signature theorem for Lipschitz manifolds. These give in particular a substitute for the usualG-signature theorem that applies to certain nonsmooth actions on topological manifolds. Then we present a number of applications. Among the most striking are a proof that ‘nonlinear similarities’ preserve ‘renormalized Atiyah-Bott numbers’, and a proof that under suitable gap, local flatness, and simple connectivity hypotheses, a compact (topological)G-manifoldM is determined up to finite ambiguity by its isovariant homotopy type and by the classes of the equivariant signature operators on all the fixed sets $$M^H ,H \subseteq G$$ . These could also be proved using joint work of Cappell, Shaneson, and the second author on topological characteristic classes.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00962083
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