Nontrivalent graph cocycle and cohomology of the long knot space

Sakai, Keiichi

doi:10.2140/agt.2008.8.1499

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Nontrivalent graph cocycle and cohomology of the long knot space

Keiichi Sakai

Algebraic & Geometric Topology 8 (2008) 1499–1522

DOI: 10.2140/agt.2008.8.1499

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

Volume 8, issue 3 (2008)