Pin(2)-equivariant KO-theory and intersection forms of spin four-manifolds

Abstract

Using 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. As an application, we give explicit constrains on the intersection forms of spin $4$-manifolds bounded by Brieskorn spheres $\pm \Sigma (2,3,6k\pm 1)$. Along the way, we also give an alternative proof of Furuta-Kametanni's improvement of 10/8-theorem for closed spin-4 manifolds.

29pages

Cited by in corpus (5)

• Khovanov homotopy type, Burnside category, and products
• A new gauge slice for the relative Bauer-Furuta invariants
• Unfolded Seiberg-Witten Floer spectra, I: Definition and invariance
• A survey of the homology cobordism group
• Positive scalar curvature and $10/8$-type inequalities on $4$-manifolds with periodic ends