Cohomology Rings of a Class of Torus Manifolds

TL;DR

This paper computes the rational cohomology rings of a specific class of torus manifolds, extending understanding of their topological structure by analyzing those with orbit spaces formed as connected sums of simple polytopes.

Contribution

It provides explicit cohomology ring calculations for a new class of torus manifolds with orbit spaces as connected sums of simple polytopes.

Findings

Explicit rational cohomology rings derived for the class of manifolds.

Identification of topological invariants related to the orbit space structure.

Extension of cohomological techniques to more complex torus manifolds.

Abstract

Torus manifolds are topological generalization of smooth projective toric manifolds. We compute the rational cohomology ring of a class of smooth locally standard torus manifolds whose orbit space is a connected sum of simple polytopes.