Twisted Donaldson invariants

Tsuyoshi Kato, Hirofumi Sasahira, Hang Wang

Research output: Contribution to journalArticlepeer-review


Fundamental group of a manifold gives a deep effect on its underlying smooth structure. In this paper we introduce a new variant of the Donaldson invariant in Yang-Mills gauge theory from twisting by the Picard group of a 4-manifold in the case when the fundamental group is free abelian. We then generalise it to the general case of fundamental groups by use of the framework of non commutative geometry. We also verify that our invariant distinguishes smooth structures between some homeomorphic 4-manifolds.

Original languageEnglish
Pages (from-to)515-568
Number of pages54
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number3
Publication statusPublished - Nov 4 2021

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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