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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