#### Volume 15, issue 2 (2015)

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

### Jianfeng Lin

Algebraic & Geometric Topology 15 (2015) 863–902
##### Abstract

Using the Seiberg–Witten Floer spectrum and $Pin\left(2\right)$–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 $±\Sigma \left(2,3,6k±1\right)$. Along the way, we also give an alternative proof of Furuta’s improvement of $\frac{10}{8}$–theorem for closed spin $4$–manifolds.

##### Keywords
Seiberg–Witten theory, $4$–manifold, equivariant KO–theory
Primary: 57R58
Secondary: 57R57