Analytical signatures and proper actions

Noé Bárcenas, Quitzeh Morales-Meléndez



We compare Mishchenko's definition of non-commutative signature for an oriented manifold with an orientation preserving proper action of a discrete, countable group $G$ with the (more analytical) counterpart defined by Higson and Roe in the series of articles ``Mapping surgery to analysis''. A generalization of the bordism invariance of the coarse index is also addressed.


Bordism invariance; Coarse index; Hilbert-Poincaré complexes

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