Realizing the analytic surgery group of Higson and Roe geometrically, part I: the geometric model
Journal article, 2017

© 2015, Tbilisi Centre for Mathematical Sciences. We construct a geometric analog of the analytic surgery group of Higson and Roe for the assembly mapping for free actions of a group with values in a Banach algebra completion of the group algebra. We prove that the geometrically defined group, in analogy with the analytic surgery group, fits into a six term exact sequence with the assembly mapping and also discuss mappings with domain the geometric group. In particular, given two finite dimensional unitary representations of the same rank, we define a map in the spirit of η-type invariants from the geometric group (with respect to assembly for the full group C ∗ -algebra) to the real numbers.

Index theory

η-invariants

Geometric K-homology

Baum-Connes

Author

R.J. Deeley

Magnus C H T Goffeng

Chalmers, Mathematical Sciences

University of Gothenburg

Journal of Homotopy and Related Structures

2193-8407 (ISSN) 1512-2891 (eISSN)

Vol. 12 1 109-142

Roots

Basic sciences

Subject Categories

Geometry

Mathematical Analysis

DOI

10.1007/s40062-015-0123-x

More information

Created

12/28/2017