Algebraic & Geometric Topology

$\mathrm{Pin}(2)$–equivariant KO–theory and intersection forms of spin $4$–manifolds

Jianfeng Lin

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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.

Article information

Algebr. Geom. Topol., Volume 15, Number 2 (2015), 863-902.

Received: 23 January 2014
Revised: 4 July 2014
Accepted: 3 August 2014
First available in Project Euclid: 28 November 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 57R58: Floer homology
Secondary: 57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]

Seiberg–Witten theory $4$–manifold equivariant KO–theory


Lin, Jianfeng. $\mathrm{Pin}(2)$–equivariant KO–theory and intersection forms of spin $4$–manifolds. Algebr. Geom. Topol. 15 (2015), no. 2, 863--902. doi:10.2140/agt.2015.15.863.

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