Semi-Infinite Cycles in Floer Theory: Viterbo's Theorem

Max Lipyanskiy

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arXiv · 0911.3714

Semi-Infinite Cycles in Floer Theory: Viterbo's Theorem

Max Lipyanskiy

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Abstract

This is the first of a series of papers on foundations of Floer theory. We give an axiomatic treatment of the geometric notion of a semi-infinite cycle. Using this notion, we introduce a bordism version of Floer theory for the cotangent bundle of a compact manifold M. Our construction is geometric and does not require the compactness and gluing results traditionally used to setup Floer theory. Finally, we prove a bordism version of Viterbo's theorem relating Floer bordism of the cotangent bundle to the ordinary bordism groups of the free loop space of M.

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Max Lipyanskiy. 2009-11-19. Semi-Infinite Cycles in Floer Theory: Viterbo's Theorem. https://arxiv.org/abs/0911.3714

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