2023/05/30 by Ismaïl Razack, Razack, Ismaïl
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2305.19054
Let X be a compact, oriented, second countable pseudomanifold. We show that HH^∗_\bullet(\widetilde N^∗_\bullet(X;ℚ)), the Hochschild cohomology of the blown-up intersection cochain complex of X, is well defined and endowed with a Batalin-Vilkovisky algebra structure. Furthermore, we prove that it is a topological invariant. More generally, we define the Hochschild cohomology of a perverse differential graded algebra A_\bullet and present a natural Gerstenhaber algebra structure on it. This structure can be extended into a Batalin-Vilkovisky algebra when A_\bullet is a derived Poincaré duality algebra.