The signature and the elliptic genus of π2-finite manifolds with circle actions

Haydeé Herrera; Rafael Herrera

doi:10.1016/S0166-8641(03)00260-8

The signature and the elliptic genus of π2-finite manifolds with circle actions

Haydeé Herrera, Rafael Herrera

Rutgers Camden, Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We prove the vanishing of various characteristic numbers, such as the signature and the ̂A-genus, on manifolds with finite second homotopy group and which admit smooth S¹-actions. More precisely, we prove the vanishing of various coefficientes of the elliptic genus on non-spin π₂-finite manifolds when the S¹-action either satisfies a "parity" condition or has isolated fixed points only.

Original language	English (US)
Pages (from-to)	251-259
Number of pages	9
Journal	Topology and its Applications
Volume	136
Issue number	1-3
DOIs	https://doi.org/10.1016/S0166-8641(03)00260-8
State	Published - Jan 28 2004

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

A-genus
Circle action
Elliptic genus
Signature

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10.1016/S0166-8641(03)00260-8

Cite this

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title = "The signature and the elliptic genus of π2-finite manifolds with circle actions",

abstract = "We prove the vanishing of various characteristic numbers, such as the signature and the{\^ }A-genus, on manifolds with finite second homotopy group and which admit smooth S1-actions. More precisely, we prove the vanishing of various coefficientes of the elliptic genus on non-spin π2-finite manifolds when the S1-action either satisfies a {"}parity{"} condition or has isolated fixed points only.",

keywords = "A-genus, Circle action, Elliptic genus, Signature",

author = "Hayde{\'e} Herrera and Rafael Herrera",

note = "Funding Information: * Corresponding author. E-mail addresses: [email protected] (H. Herrera), [email protected] (R. Herrera). 1 Partially supported by a Guggenheim Fellowship, NSF grant DMS-0204002, and PSC-CUNY grant #60031-33-34.",

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T1 - The signature and the elliptic genus of π2-finite manifolds with circle actions

AU - Herrera, Haydeé

AU - Herrera, Rafael

N1 - Funding Information: * Corresponding author. E-mail addresses: [email protected] (H. Herrera), [email protected] (R. Herrera). 1 Partially supported by a Guggenheim Fellowship, NSF grant DMS-0204002, and PSC-CUNY grant #60031-33-34.

PY - 2004/1/28

Y1 - 2004/1/28

N2 - We prove the vanishing of various characteristic numbers, such as the signature and the ̂A-genus, on manifolds with finite second homotopy group and which admit smooth S1-actions. More precisely, we prove the vanishing of various coefficientes of the elliptic genus on non-spin π2-finite manifolds when the S1-action either satisfies a "parity" condition or has isolated fixed points only.

AB - We prove the vanishing of various characteristic numbers, such as the signature and the ̂A-genus, on manifolds with finite second homotopy group and which admit smooth S1-actions. More precisely, we prove the vanishing of various coefficientes of the elliptic genus on non-spin π2-finite manifolds when the S1-action either satisfies a "parity" condition or has isolated fixed points only.

KW - A-genus

KW - Circle action

KW - Elliptic genus

KW - Signature

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U2 - 10.1016/S0166-8641(03)00260-8

DO - 10.1016/S0166-8641(03)00260-8

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AN - SCOPUS:0344082815

SN - 0166-8641

VL - 136

SP - 251

EP - 259

JO - Topology and its Applications

JF - Topology and its Applications

IS - 1-3

ER -

The signature and the elliptic genus of π2-finite manifolds with circle actions

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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