Browsing Mathematics Theses and Dissertations by Author "Sinha, Dev"
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Chettih, Safia (University of Oregon, November 21, 2016)[more][less]Sinha, Dev Chettih, Safia 20161121T17:00:59Z 20161121T17:00:59Z 20161121 http://hdl.handle.net/1794/20728 We prove that the nonkequal configuration space of a graph has a discretized model, analogous to the discretized model for configurations on graphs. We apply discrete Morse theory to the latter to give an explicit combinatorial formula for the ranks of homology and cohomology of configurations of two points on a tree. We give explicit presentations for homology and cohomology classes as well as pairings for ordered and unordered configurations of two and three points on a few simple trees, and show that the first homology group of ordered and unordered configurations of two points in any tree is generated by the first homology groups of configurations of two points in three particular graphs, K_{1,3}, K_{1,4}, and the trivalent tree with 6 vertices and 2 vertices of degree 3, via graph embeddings. en_US University of Oregon All Rights Reserved. configuration space discrete Morse theory graph braid group nonkequal configuration Dancing in the Stars: Topology of Nonkequal Configuration Spaces of Graphs Electronic Thesis or Dissertation Ph.D. doctoral Department of Mathematics University of Oregon

Pelatt, Kristine (University of Oregon, 2012)[more][less]Sinha, Dev Pelatt, Kristine Pelatt, Kristine 20121026T04:03:49Z 20121026T04:03:49Z 2012 http://hdl.handle.net/1794/12423 We produce explicit geometric representatives of nontrivial homology classes in Emb(S1,Rd), the space of knots, when d is even. We generalize results of Cattaneo, CottaRamusino 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 nontrivially 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. en_US University of Oregon All Rights Reserved. embedding spaces spaces of knots Geometry and Combinatorics Pertaining to the Homology of Spaces of Knots Electronic Thesis or Dissertation
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