Simple-type conjecture for Seiberg–Witten invariants

Let XX be a manifold of simple type. For a choice of SpincSpin_c-structure LL, let MLM_L be the Seiberg–Witten moduli space and let d=dim(ML)d=\dim(M_L). Simple-type conjecture. The only non-trivial Seiberg–Witten invariants correspond to choices of LL such that

d=dim(ML)=0.d=\dim(M_L)=0.

This conjecture asserts that positive-dimensional Seiberg–Witten moduli spaces do not contribute non-trivial invariants for manifolds of simple type. The source calls it a related conjecture but provides no resolution evidence.

Sources & referencesView supporting material

Primary source

M. Marcolli, “Notes on Seiberg-Witten Gauge Theory”, arXiv:dg-ga/9509005 (1995).

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