Nontrivalent graph cocycle and cohomology of the long knot space

Sakai, Keiichi¹

¹Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan

Algebraic and Geometric Topology, Tome 8 (2008) no. 3, pp. 1499-1522

Résumé

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.

Détail

DOI : 10.2140/agt.2008.8.1499

Keywords: long knot, configuration space integral, graph cohomology, little disks operad

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