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The integral cohomology of the group of loops

Craig A Jensen, Jon McCammond and John Meier

Geometry & Topology 10 (2006) 759–784

DOI: 10.2140/gt.2006.10.759

arXiv: 0903.0140
Abstract

Let PΣn denote the group that can be thought of either as the group of motions of the trivial n–component link or the group of symmetric automorphisms of a free group of rank n. The integral cohomology ring of PΣn is determined, establishing a conjecture of Brownstein and Lee.

Keywords

nonpositive curvature, CAT(0), decidability
Mathematical Subject Classification

Primary: 20J06

Secondary: 57M07
References
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Publication

Received: 16 October 2005
Revised: 6 February 2006
Accepted: 3 June 2006
Published: 11 July 2006
Proposed: Benson Farb
Seconded: Joan Birman, Walter Neumann
Authors
Craig A Jensen
Department of Mathematics
University of New Orleans
New Orleans, LA 70148
USA
Jon McCammond
Department of Mathematics
University of California
Santa Barbara, CA 93106
USA
John Meier
Deptartment of Mathematics
Lafayette College
Easton, PA 18042
USA