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.
| Identifer | oai:union.ndltd.org:uoregon.edu/oai:scholarsbank.uoregon.edu:1794/12423 |
| Date | January 2012 |
| Creators | Pelatt, Kristine, Pelatt, Kristine |
| Contributors | Sinha, Dev |
| Publisher | University of Oregon |
| Source Sets | University of Oregon |
| Language | en_US |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Rights | All Rights Reserved. |
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