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Geometry and Combinatorics Pertaining to the Homology of Spaces of Knots

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.

Identiferoai:union.ndltd.org:uoregon.edu/oai:scholarsbank.uoregon.edu:1794/12423
Date January 2012
CreatorsPelatt, Kristine, Pelatt, Kristine
ContributorsSinha, Dev
PublisherUniversity of Oregon
Source SetsUniversity of Oregon
Languageen_US
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
RightsAll Rights Reserved.

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