2021/01/10 by Vivek Shende, Shende, Vivek
Mathematics · #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2101.03469
openalex publication_date 2021/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.