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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
On the intersection forms of spin 4–manifolds bounded by spherical 3–manifolds

Masaaki Ue

Algebraic & Geometric Topology 1 (2001) 549–578

arXiv: math.GT/0110179

Abstract

We determine the contributions of isolated singularities of spin V 4–manifolds to the index of the Dirac operator over them. From these data we derive certain constraints on the intersection forms of spin 4–manifolds bounded by spherical 3–manifolds, and also on the embeddings of the real projective planes into 4–manifolds.

Keywords
spin 4–manifold, spherical 3–manifold, Dirac operator
Mathematical Subject Classification 2000
Primary: 57N13
Secondary: 57M50, 57M60
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Publication
Received: 18 July 2001
Revised: 5 October 2001
Accepted: 5 October 2001
Published: 14 October 2001
Authors
Masaaki Ue
Division of Mathematics
Faculty of Integrated Human Studies
Kyoto University
Kyoto
606-8316
Japan