Volume 12, issue 2 (2012)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Von Neumann rho invariants and torsion in the topological knot concordance group

Christopher William Davis

Algebraic & Geometric Topology 12 (2012) 753–789
Abstract

We discuss an infinite class of metabelian Von Neumann ρ–invariants. Each one is a homomorphism from the monoid of knots to . In general they are not well defined on the concordance group. Nonetheless, we show that they pass to well defined homomorphisms from the subgroup of the concordance group generated by anisotropic knots. Thus, the computation of even one of these invariants can be used to conclude that a knot is of infinite order. We introduce a method to give a computable bound on these ρ–invariants. Finally we compute this bound to get a new and explicit infinite set of twist knots which is linearly independent in the concordance group and whose every member is of algebraic order 2.

Keywords
knot concordance, rho-invariants
Mathematical Subject Classification 2010
Primary: 57M25, 57M27, 57N70
References
Publication
Received: 16 February 2011
Revised: 28 September 2011
Accepted: 28 September 2011
Published: 12 April 2012
Authors
Christopher William Davis
Department of Mathematics
Rice University
6100 Main St
Houston TX 77005
USA
http://math.rice.edu/~cwd1/