2008/02/29 by Raphael Zentner, Zentner, Raphael
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT
paper · pdf · doi:10.48550/arxiv.0803.0025
23 pages
arxiv created 2008/02/29 · openalex publication_date 2008/02/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A famous conjecture in gauge theory mathematics, attributed to Witten, suggests that the polynomial invariants of Donaldson are expressible in terms of the Seiberg-Witten invariants if the underlying four-manifold is of simple type. Mathematicians have sought a proof of the conjecture by means of a `cobordism program' involving PU(2) monopoles. A higher rank version of the Donaldson invariants was recently introduced by Kronheimer. Before being defined, the physicists Mariño and Moore had already suggested that there should be a generalisation of Witten's conjecture to this type of invariants. We adopt a generalisation of the cobordism program to the higher rank situation by studying PU(N) monopoles. We analyse the differences to the PU(2) situation, yielding evidence that a generalisation of Witten's conjecture should hold.