BV-structures on the homology of the framed long knot space

作者：Sakai Keiichi^*

来源：Journal of Homotopy and Related Structures, 2016, 11(3): 425-441.

DOI：10.1007/s40062-015-0111-1

• Space of long knots
• BV algebra
• Hatcher's cycle
• Hochschild homology
• Connes' boundary operator

We introduce BV-algebra structures on the homology of the space of framed long knots in in two ways. The first one is given in a similar fashion to Chas-Sullivan's string topology. The second one is defined on the Hochschild homology associated with a cyclic, multiplicative operad of graded modules. The latter can be applied to Bousfield-Salvatore spectral sequence converging to the homology of the space of framed long knots. Conjecturally these two structures coincide with each other.

• 出版日期2016-9