Speaker: Robin Koytcheff (University of Louisiana at Lafayette)

Abstract:  In joint work with Yongheng Zhang, we define an action of an operad of cacti on the Taylor tower for the space of framed 1-dimensional long knots in any Euclidean space.  We prove a certain compatibility of our action with Budney's little 2-cubes action on the space of framed long knots itself.  Our result improves upon previous joint work with Budney, Conant, and Sinha on the conjecture that the Taylor tower is a universal Vassiliev invariant over the integers.  We are currently using our compatibility result to detect Browder brackets of known classes, including a class found by Sakai, as well as potentially new ones.