Periodic Symplectic Cohomologies

2014/05/08 by Zhao, Jingyu · 1 citation
#FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1405.2084

Abstract

Goodwillie \citeGoodwillie 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^*_S¹(M) and HP^*_{S¹, loc}(M). Our main result is that both cohomology theories are invariant under Liouville isomorphisms and there is a natural isomorphism HP^*_{S¹, loc}(M, ℚ) ≅ H^*(M, ℚ)((u)), which can be seen as a localization theorem for HP^*_{S¹, loc}(M, ℚ).

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