An algebraic approach to the algebraic Weinstein conjecture

Vivek Shende*


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How does one measure the failure of Hochschild homology to commute with colimits? Here, I relate this question to a major open problem about dynamics in contact manifolds—the assertion that Reeb orbits exist and are detected by symplectic homology. More precisely, I show that for polarizably Weinstein fillable contact manifolds, said property is equivalent to the failure of Hochschild homology to commute with certain colimits of representation categories of tree quivers. So as to be intelligible to algebraists, I try to include or black-box as much of the geometric background as possible.

TidsskriftJournal of Fixed Point Theory and Applications
Udgave nummer2
StatusUdgivet - jun. 2022

Bibliografisk note

Funding Information:
Beyond the evident intellectual debt that this work owes to the ideas of Claude Viterbo, it happens that I was inspired to write it by the upcoming celebration of his mathematics on the occasion of his sixtieth birthday.

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.


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