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Twisted Donaldson invariants
- Source :
- Mathematical Proceedings of the Cambridge Philosophical Society. 171:515-568
- Publication Year :
- 2021
- Publisher :
- Cambridge University Press (CUP), 2021.
-
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.<br />Comment: typos fixed, Rewrite Section 4 to reduce technicality
- 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
Subjects
Details
- ISSN :
- 14698064 and 03050041
- Volume :
- 171
- Database :
- OpenAIRE
- Journal :
- Mathematical Proceedings of the Cambridge Philosophical Society
- Accession number :
- edsair.doi.dedup.....c413ff305749905e38fafd1ca5d82fa5