Algebraic and Geometric Topology 1 (2001), paper no. 28, pages 549-578.

On the intersection forms of spin 4-manifolds bounded by spherical 3-manifolds

Masaaki Ue

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

AMS subject classification. Primary: 57N13. Secondary: 57M50, 57M60.

DOI: 10.2140/agt.2001.1.549

E-print: arXiv:math.GT/0110179

Submitted: 18 July 2001. (Revised: 5 October 2001.) Accepted: 5 October 2001. Published: 14 October 2001.

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Masaaki Ue
Division of Mathematics, Faculty of Integrated Human Studies
Kyoto University, Kyoto, 606-8316, Japan
Email: ue@math.h.kyoto-u.ac.jp

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