Volume 8, issue 3 (2008)

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
Nontrivalent graph cocycle and cohomology of the long knot space

Keiichi Sakai

Algebraic & Geometric Topology 8 (2008) 1499–1522
Abstract

In this paper we show that via the configuration space integral construction a nontrivalent graph cocycle can also yield a nonzero cohomology class of the space of higher (and even) codimensional long knots. This simultaneously proves that the Browder operation induced by the operad action defined by R Budney is not trivial.

Keywords
long knot, configuration space integral, graph cohomology, little disks operad
Mathematical Subject Classification 2000
Primary: 58D10
Secondary: 55P48, 81Q30
References
Publication
Received: 31 December 2007
Revised: 18 July 2008
Accepted: 18 July 2008
Published: 5 September 2008
Authors
Keiichi Sakai
Graduate School of Mathematical Sciences
The University of Tokyo
3-8-1 Komaba, Meguro
Tokyo 153-8914
Japan