Let X(Q, Λ) be a quasitoric manifold associated to a simple convex polytope Q and characteristic function Λ. Let T≅(S1)n denote the compact n-torus acting on X= X(Q, Λ). The main aim of this article is to give a presentation of the T-equivariant K-ring of X, as a Stanley–Reisner ring over K∗(pt). We also derive the presentation for the ordinary K-ring of X. © 2019, Indian Academy of Sciences.

V Uma

Department of Mathematics

CHARACTERISTIC FUNCTIONS

Convex polytopes

Face ring

K-THEORY

Mathematical techniques

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IIT Madras

Proceedings of the Indian Academy of Sciences: Mathematical Sciences

Let X be a 2n-dimensional torus manifold with a locally standard T ≅ (S1)n action whose orbit space is a homology polytope. Smooth complete complex toric varieties and quasitoric manifolds are examples of torus manifolds. Consider a principal T-bundle p : E → B and let π: E(X) → B be the associated torus manifold bundle. We give a presentation of the singular cohomology ring of E(X) as a H∗(B)-algebra and the topological K-ring of E(X) as a K∗(B)-algebra with generators and relations. These generalize the results in [17] and [19] when the base B = pt. These also extend the results in [20], obtained in the case of a smooth projective toric variety, to any smooth complete toric variety. © 2019 Mathematical Institute Slovak Academy of Sciences.

Fulltext

Mathematica Slovaca

Cohomology of torus manifold bundles

Tohoku Mathematical Journal

The equivariant $K$-theory and cobordism rings of divisive weighted projective spaces

Transactions of the American Mathematical Society

Surjectivity for Hamiltonian $G$-spaces in $K$-theory

Equivariant K-theory of smooth toric varieties

Advances in Mathematics

Computation of generalized equivariant cohomologies of Kac–Moody flag varieties

Equivariant K -theory of quasitoric manifolds

Journal	Data powered by TypesetProceedings of the Indian Academy of Sciences: Mathematical Sciences
Publisher	Data powered by TypesetSpringer
ISSN	02534142
Open Access	No