arXiv subjects

Vikraman Uma

Publications and source records attributed to Vikraman Uma.

5 recordsLinked to original sources

arXiv2024

Equivariant $K$-theory of Springer Varieties

The aim of this paper is to describe the topological equivariant $K$-ring, in terms of generators and relations, of a Springer variety $\mathcal{F}_λ$ of type $A$ associated to a nilpotent operator having Jordan canonical form whose block sizes form a weakly decreasing sequence $λ=(λ_1,\ldots, λ_l)$. This parallels the description of the equivariant cohomology ring of $\mathcal{F}_λ$ due to Abe and Horiguchi and generalizes the description of ordinary topological $K$-ring of $\mathcal{F}_λ$ due to Sankaran and Uma \cite{su}.

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arXiv2023

$K$-theory of Flag Bott manifolds

The aim of this paper is to describe the topological $K$-ring, in terms of generators and relations of a flag Bott manifold. We apply our results to give a presentation for the topological K-ring and hence the Grothendieck ring of algebraic vector bundles over flag Bott Samelson varieties.

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arXiv2023

K-theory of Springer varieties

The aim of this paper is to describe the topological $K$-ring, in terms of generators and relations, of a Springer variety $\mathcal{F}_λ$ of type $A$ associated to a nilpotent operator having Jordan canonical form whose block sizes form a weakly decreasing sequence $λ=(λ_1,\ldots, λ_l)$. Our description parallels the description of the integral cohomology ring of $\mathcal{F}_λ$ due to Tanisaki and also the equivariant analogue due to Abe and Horiguchi.

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arXiv2022

Equivariant $K$-theory of flag Bott manifolds of general Lie type

The aim of this paper is to describe the equivariant and ordinary Grothendieck ring and the equivariant and ordinary topological $K$-ring of flag Bott manifolds of general Lie type. This will generalize the results on the equivariant and ordinary cohomology of flag Bott manifolds of general Lie type due to Kaji Kuroki Lee and Suh.

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arXiv2021

GKM graph locally modeled by $T^{n}\times S^{1}$-action on $T^{*}\mathbb{C}^{n}$ and its graph equivariant cohomology

We introduce a class of labeled graphs (with legs) which contains two classes of GKM graphs of $4n$-dimensional manifolds with $T^{n}\times S^{1}$-actions, i.e., GKM graphs of the toric hyperK${\rm\ddot{a}}$hler manifolds and of the cotangent bundles of toric manifolds. Under some conditions, the graph equivariant cohomology ring of such a labeled graph is computed. We also give a module basis of the graph equivariant cohomology by using a shelling structure of such a labeled graph and study their multiplicative structure.

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