Manolescu invariants of connected sums. Issue 5 (14th August 2017)

• Record Type: Journal Article
• Authors: Stoffregen, Matthew
• Is Part Of: Proceedings of the London Mathematical Society. Volume 115:Issue 5(2017)
• Page Start: 1072
• Page End: 1117
• Publication Date: 2017-08-14
• Subjects: 57R58 -- 57M25 (primary); Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1112/plms.12060
• Languages: English
• ISSNs: 0024-6115

Abstract

Abstract: We give inequalities for the Manolescu invariants α, β, γ under the connected sum operation. We compute the Manolescu invariants of connected sums of some Seifert fiber spaces. Using these same invariants, we provide a proof of Furuta's Theorem, the existence of a Z ∞ subgroup of the homology cobordism group. To our knowledge, this is the first proof of Furuta's Theorem using monopoles. We also provide information about Manolescu invariants of the connected sum of n copies of a three‐manifold Y, for large n .