Vafa's formula and equivariant \(K\)-theory
type: Item
instance of: scholarly article
title: Vafa's formula and equivariant \(K\)-theory
zbMATH Open document ID: 0786.55003
DOI: 10.1016/0393-0440(93)90020-F
author: Kaoru Ono
author: Shi-Shyr Roan
published in: Journal of Geometry and Physics
publication date: 1994-05-05T00:00:00Z
review text: Let \(X\) be a quasi-smooth hypersurface in weighted projective space defined by a quasi-homogeneous one of degree \(d\). The natural projection restricted over \(X\) gives rise to a Seifert fibration from \(S_ X\) to the weighted projective space. The Euler characteristic of \(S^ 1\)- equivariant \(K\)-theory of \(S_ X\), that is \(\text{rank }K_{S^ 1}^ 0(S_ X)- \text{rank } K_{S^ 1}^ 1(S_ X)\), is equal to an expression which contains a term that has the same form as Vafa's expression of Witten's index.
Mathematics Subject Classification ID: 55N15
Mathematics Subject Classification ID: 19L47
Mathematics Subject Classification ID: 81T99
zbMATH DE Number: 205508
zbMATH Keywords: equivariant \(K\)-theory
zbMATH Keywords: Seifert fibration
zbMATH Keywords: Euler characteristic
zbMATH Keywords: Witten's index
reviewed by: Daniel H. Gottlieb
MaRDI profile type: Publication
cites work: On equivariant Euler characteristics
cites work: On the Euler number of an orbifold
cites work: Description of a class of superstring compactifications related to semi- simple Lie algebras
cites work: On the generalization of Kummer surfaces
cites work: ON CALABI-YAU ORBIFOLDS IN WEIGHTED PROJECTIVE SPACES
cites work: THE MIRROR OF CALABI-YAU ORBIFOLD
cites work: Equivariant K-theory
full work available at URL: 0393-0440(93)90020-f
OpenAlex ID: W1976656781
description: scientific article; zbMATH DE number 205508