Geometry and Combinatorics Pertaining to the Homology of Spaces of Knots

Show full item record

Title: Geometry and Combinatorics Pertaining to the Homology of Spaces of Knots
Author: Pelatt, Kristine
Abstract: We produce explicit geometric representatives of non-trivial homology classes in Emb(S1,Rd), the space of knots, when d is even. We generalize results of Cattaneo, Cotta-Ramusino and Longoni to define cycles which live off of the vanishing line of a homology spectral sequence due to Sinha. We use con figuration space integrals to show our classes pair non-trivially with cohomology classes due to Longoni. We then give an alternate formula for the first differential in the homology spectral sequence due to Sinha. This differential connects the geometry of the cycles we define to the combinatorics of the spectral sequence. The new formula for the differential also simplifies calculations in the spectral sequence.
URI: http://hdl.handle.net/1794/12423
Date: 2012


Files in this item

Files Size Format View
Pelatt_oregon_0171A_10414.pdf 1.296Mb PDF View/Open

This item appears in the following Collection(s)

Show full item record