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

R.J. Deeley ; Magnus Goffeng (Institutionen för matematiska vetenskaper)
Journal of Homotopy and Related Structures Vol. 12 (2017), 1, p. 109-142.
[Artikel, refereegranskad vetenskaplig]

© 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.

Nyckelord: Baum-Connes , Geometric K-homology , Index theory , η-invariants



Denna post skapades 2017-12-28.
CPL Pubid: 254149

 

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Institutionen för matematiska vetenskaperInstitutionen för matematiska vetenskaper (GU)

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Matematisk analys
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