151. Twisted Donaldson invariants
- Author
-
Hang Wang, Hirofumi Sasahira, and Tsuyoshi Kato
- Subjects
Mathematics - Differential Geometry ,Fundamental group ,Pure mathematics ,010308 nuclear & particles physics ,General Mathematics ,Mathematics - Operator Algebras ,Picard group ,Geometric Topology (math.GT) ,Mathematics::Geometric Topology ,01 natural sciences ,Manifold ,Mathematics - Geometric Topology ,Differential Geometry (math.DG) ,0103 physical sciences ,FOS: Mathematics ,57R55, 57R57, 58B34, 46L87 ,Mathematics::Differential Geometry ,Gauge theory ,Abelian group ,Invariant (mathematics) ,Operator Algebras (math.OA) ,Mathematics::Symplectic Geometry ,Commutative property ,Smooth structure ,Mathematics - Abstract
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 four manifold in the case when the fundamental group is free abelian. We then generalize 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 four manifolds., Comment: typos fixed, Rewrite Section 4 to reduce technicality
- Published
- 2021