Mathematische Annalen

, Volume 359, Issue 3–4, pp 695–728 | Cite as

On the intersection forms of spin four-manifolds with boundary



We prove Furuta-type bounds for the intersection forms of spin cobordisms between homology 3-spheres. The bounds are in terms of a new numerical invariant of homology spheres, obtained from \(\mathrm{Pin }(2)\)-equivariant Seiberg-Witten Floer K-theory. In the process we introduce the notion of a Floer \(K_G\)-split homology sphere; this concept may be useful in an approach to the 11/8 conjecture.

Mathematics Subject Classification (2000)

57R58 57R57 



This research was partially supported by NSF grant DMS-1104406. I would like to thank Mike Hopkins, Peter Kronheimer and Ron Stern for some very enlightening conversations, and the Simons Center for Geometry and Physics (where part of this work was written) for its hospitality. I am also grateful to Jianfeng Lin, Brendan Owens and the referee for comments on a previous version of this paper. Some of the results in this article have been obtained independently by Mikio Furuta and Tian-Jun Li [20].


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of MathematicsUCLALos AngelesUSA

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