Algebraic & Geometric Topology

A finite-dimensional approach to the strong Novikov conjecture

Abstract

The aim of this paper is to describe an approach to the (strong) Novikov conjecture based on continuous families of finite-dimensional representations: this is partly inspired by ideas of Lusztig related to the Atiyah–Singer families index theorem, and partly by Carlsson’s deformation $K$–theory. Using this approach, we give new proofs of the strong Novikov conjecture in several interesting cases, including crystallographic groups and surface groups. The method presented here is relatively accessible compared with other proofs of the Novikov conjecture, and also yields some information about the $K$–theory and cohomology of representation spaces.

Article information

Source
Algebr. Geom. Topol., Volume 13, Number 4 (2013), 2283-2316.

Dates
Revised: 29 January 2013
Accepted: 19 March 2013
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715639

Digital Object Identifier
doi:10.2140/agt.2013.13.2283

Mathematical Reviews number (MathSciNet)
MR3073917

Zentralblatt MATH identifier
1277.19002

Citation

Ramras, Daniel; Willett, Rufus; Yu, Guoliang. A finite-dimensional approach to the strong Novikov conjecture. Algebr. Geom. Topol. 13 (2013), no. 4, 2283--2316. doi:10.2140/agt.2013.13.2283. https://projecteuclid.org/euclid.agt/1513715639

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