Applications of the Ochanine genus
type: Item
instance of: scholarly article
title: Applications of the Ochanine genus
zbMATH Open document ID: 0706.57013
DOI: 10.1007/BF02571354
author: Martin Bendersky
published in: Mathematische Zeitschrift
publication date: 1992-06-25T00:00:00Z
full work available at URL: https://eudml.org/doc/174236
review text: The Ochanine genus from Spin bordism to KO theory is shown to vanish on a Spin manifold with odd type, semifree circle action. This implies the vanishing of the Brown-Kervaire invariant for many Spin manifolds. A formula is derived for the Ochanine genus of a Spin manifold with an even type, free action.
Mathematics Subject Classification ID: 57R15
Mathematics Subject Classification ID: 57R20
Mathematics Subject Classification ID: 57R90
Mathematics Subject Classification ID: 55N15
zbMATH DE Number: 958
zbMATH Keywords: Spin manifold with odd type semi-free circle action
zbMATH Keywords: Spin manifold with an even type free action
zbMATH Keywords: Ochanine genus from Spin bordism to KO theory
zbMATH Keywords: Brown-Kervaire invariant
MaRDI profile type: Publication
cites work: The Lefschetz theorem on hyperplane sections
cites work: Riemann surfaces and spin structures
cites work: Riemann-Roch theorems for differentiable manifolds
cites work: The index of elliptic operators. III
cites work: Bordism of Semifree Circle Actions on Spin Manifolds
cites work: On the Rigidity Theorems of Witten
cites work: Generalizations of the Kervaire invariant
cites work: Circle actions on spin manifolds and characteristic numbers
cites work: Sur les genres multiplicatifs définis par des intégrales elliptiques. (On multiplicative genera defined by elliptic integrals)
cites work: Elliptic genera, modular forms over \(KO_ *\), and the Brown-Kervaire invariant
cites work: Towards algebraic cobordism
cites work: Q5571606
cites work: Elliptic genera and quantum field theory
description: scientific article; zbMATH DE number 958