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arXiv · 1405.2084

Periodic Symplectic Cohomologies

Jingyu Zhao
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Abstract

Goodwillie \cite{Goodwillie} introduced a periodic cyclic homology group associated to a mixed complex. In this paper, we apply this construction to the symplectic cochain complex of a Liouville domain $M$ and obtain two periodic symplectic cohomology theories, denoted as $HP^*_{S^1}(M)$ and $HP^*_{S^1, \mathrm{loc}}(M)$. Our main result is that both cohomology theories are invariant under Liouville isomorphisms and there is a natural isomorphism $HP^*_{S^1, \mathrm{loc}}(M, \mathbb{Q}) \cong H^*(M, \mathbb{Q})((u))$, which can be seen as a localization theorem for $HP^*_{S^1, \mathrm{loc}}(M, \mathbb{Q})$.

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Jingyu Zhao. 2014-05-08. Periodic Symplectic Cohomologies. https://arxiv.org/abs/1405.2084

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