Product formulas along $T^3$ for Seiberg-Witten invariants

• DOI: 10.4310/mrl.1997.v4.n6.a11
• Publication Date: 2013-08-30T23:46:25Z
• Authors: John W. Morgan; Tomasz S. Mrowka; Zoltán Szabó
• Keywords: 0101 mathematics; 01 natural sciences

Remark 1.2.• We choose an orientation of det(H 2 ≥0 (M, ∂M, R))⊗(det(H 1 R))) -1 called a homology ∂M ).Standard Mayer-Vietoris arguments show that for ) induces M γ , i.e. det, and hence orients the moduli spaces allowing us to define function SW .In statement theorem all functions etc. are computed using orientations derived from common ).• If b + (M ≥ 2, then there no chamber structures invariants.).This identification cohomology positive cones with their structures., set spin c -structures over which we sum is exactly whose wall agrees L 0 .It in this sense, compute invariants corresponding chambers.Note, if i * (γ) indivisible, where : H (∂M, Z) → Z), left hand side above formula consists only one term, consequently get computing terms .So case Theorem 1.1 provides useful tool Seiberg-Witten invariants.For applications along these lines, see [FS3],[Sz1] [Sz2].By cylindrical end 3.1 relative C M,∂M Z, defined as follows:Let K S denote product spin-structure i.e.K represents non-trivial element 1-dimensional cobordism group.Then (K) 3 T invariant under self-diffeomorphisms such gives well-defined -structure .Now let isomorphism classes pairs consisting L| .Note similarly closed have map :is bijection, w second Stiefel-Whitney class determined by .We say ∈ basic c(L) = (L) 0. L∈c (L).Similarly case, finite.