Moscow Mathematical Journal

Volume 24, Issue 2, April–June 2024 pp. 287–315.

On Cohomology of Quasitoric Manifolds over a Vertex Cut of a Finite Product of Simplices

Authors: Soumen Sarkar (1) and Subhankar Sau (2)
Author institution:(1) Department of Mathematics, Indian Institute of Technology Madras, India
(2) Department of Mathematics, The Institute of Mathematical Sciences, Chennai, India

Summary:

In this paper, we classify the characteristic matrices associated to quasitoric manifolds over a vertex cut of a finite product of simplices satisfying a ‘sign condition’. We discuss the integral cohomology rings of these quasitoric manifolds with possibly minimal generators and show several relations among the products of these generators. We classify integral cohomology rings (up to isomorphism as graded rings) of the quasitoric manifolds over the vertex cut of a finite product of simplices.

2020 Math. Subj. Class. 57S12, 13F55, 14M25, 52B11, 55N10.

Keywords: Torus action, quasitoric manifold, vertex cut, cohomology ring.

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