Geodesic
Pin(2)–equivariant KO–theory and intersection forms of spin 4–manifolds
Lin, Jianfeng1
1Department of Mathematics, University of California Los Angeles, 405 Hilgard Avenue, Los Angeles, CA 90095-1555, USA
Algebraic and Geometric Topology, Tome 15 (2015) no. 2, pp. 863-902
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Using the Seiberg–Witten Floer spectrum and Pin(2)–equivariant KO–theory, we prove new Furuta-type inequalities on the intersection forms of spin cobordisms between homology 3–spheres. We then give explicit constrains on the intersection forms of spin 4–manifolds bounded by Brieskorn spheres ± Σ(2,3,6k ± 1). Along the way, we also give an alternative proof of Furuta’s improvement of 10 8 –theorem for closed spin 4–manifolds.

DOI : 10.2140/agt.2015.15.863
Classification : 57R58, 57R57
Keywords: Seiberg–Witten theory, $4$–manifold, equivariant KO–theory

Lin, Jianfeng  1

1 Department of Mathematics, University of California Los Angeles, 405 Hilgard Avenue, Los Angeles, CA 90095-1555, USA 
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Lin, Jianfeng. Pin(2)–equivariant KO–theory and intersection forms of spin 4–manifolds. Algebraic and Geometric Topology, Tome 15 (2015) no. 2, pp. 863-902. doi: 10.2140/agt.2015.15.863

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