Volume 8, issue 3 (2008)

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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