The signature and the elliptic genus of \(\pi_{2}\)-finite manifolds with circle actions.

DOI10.1016/S0166-8641(03)00260-8zbMath1039.57018MaRDI QIDQ1421998

Rafael Herrera, Haydeé Herrera

Publication date: 3 February 2004

Published in: Topology and its Applications (Search for Journal in Brave)

zbMATH Keywords

fixed pointscircle actionhomotopy groupsignaturerepresentationDirac operatorrigidityelliptic genus\(\pi_ 2\)-finite manifoldÂ-genusnon-spin manifoldPontrjagin characteristic numbers

Mathematics Subject Classification ID

Groups acting on specific manifolds (57S25) Compact Lie groups of differentiable transformations (57S15) Characteristic classes and numbers in differential topology (57R20) Elliptic genera (58J26) Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) (57R15)

Related Items (4)

Rigidity and vanishing theorems for almost quaternionic manifolds ⋮ Positively curved \(\pi_2\)-finite manifolds ⋮ Erratum to ``The signature and the elliptic genus of \(\pi_2\)-finite manifolds with circle actions ⋮ Torus actions of generalized odd type on oriented manifolds

Cites Work

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• Elliptic genera and quantum field theory
• A result on the \(\widehat A\) and elliptic genera on non-spin manifolds with circle actions
• Elliptic genera, involutions, and homogeneous spin manifolds
• Geometric diffeomorphism finiteness in low dimensions and homotopy group finiteness
• Classification of positive quaternion-Kähler 12-manifolds
• \(\hat A\)-genus on non-spin manifolds with \(S^ 1\) actions and the classification of positive quaternion-Kähler 12-manifolds.
• Diffeomorphism finiteness, positive pinching, and second homotopy
• \(S^ 1\)-actions and elliptic genera
• Representations at fixed points of smooth actions of compact groups
• The index of elliptic operators. III
• On the Rigidity Theorems of Witten
• Homotopical Properties of Fixed Point Sets of Circle Group Actions, I

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