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Transversal String Topology and Invariants of Manifolds

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dc.contributor.advisor Dennis P. Sullivan. en_US
dc.contributor.author Basu, Somnath en_US
dc.contributor.other Department of Mathematics en_US
dc.date.accessioned 2012-05-17T12:19:48Z
dc.date.accessioned 2015-04-24T14:47:55Z
dc.date.available 2012-05-17T12:19:48Z
dc.date.available 2015-04-24T14:47:55Z
dc.date.issued 2011-08-01 en_US
dc.identifier Basu_grad.sunysb_0771E_10683.pdf en_US
dc.identifier.uri http://hdl.handle.net/1951/55954 en_US
dc.identifier.uri http://hdl.handle.net/11401/71559 en_US
dc.description.abstract Loop spaces have played a recurring and important role in mathematics - from closed geodesics in differential geometry to based loop spaces which play a central role in homotopy theory. The subject of string topology originating from the seminal paper by Chas and Sullivan, focuses on topological aspects of the free loop space of manifolds; it's the study of the algebraic structures present therein. From the point of view of computations, several techniques of algebraic topology may apply. We show, using rational homotopy theory and minimal models, that the Lie algebra structure on the (circle) equivariant homology of a product of odd spheres is highly non-trivial although the same structure for an odd sphere is trivial. Similar smaller computational results are also presented. In the main result of this work, we define and study certain geometric loops, called transversal strings, which satisfy some specific boundary conditions. The relevant algebraic backdrop happens to be the category of bicomodules and algebra objects in this setting. Using the machinery of minimal models and homological algebra in this setting, we show that using transversal string topology it's possible to distinguish non-homeomorphic but homotopy equivalent Lens spaces. en_US
dc.description.sponsorship This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. en_US
dc.format Monograph en_US
dc.format.medium Electronic Resource en_US
dc.language.iso en_US en_US
dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US
dc.subject.lcsh Mathematics en_US
dc.subject.other Algebraic topology, Bicomodules, Configuration space, Loop space, String topology, Transversal strings en_US
dc.title Transversal String Topology and Invariants of Manifolds en_US
dc.type Dissertation en_US
dc.mimetype Application/PDF en_US
dc.contributor.committeemember John Morgan en_US
dc.contributor.committeemember Oleg Viro en_US
dc.contributor.committeemember Mahmoud Zeinalian en_US


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