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

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.

η-invariants

Index theory

Baum-Connes

Geometric K-homology

Author

R.J. Deeley

University of Hawaii

Magnus C H T Goffeng

University of Hanover

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

Latest update

5/10/2021