An SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg-Witten Invariants Paperback / softback
by Paul Feehan, Thomas G. Leness
Part of the Memoirs of the American Mathematical Society series
Paperback / softback
Description
The authors prove an analogue of the Kotschick-Morgan Conjecture in the context of $\mathrm{SO(3)}$ monopoles, obtaining a formula relating the Donaldson and Seiberg-Witten invariants of smooth four-manifolds using the $\mathrm{SO(3)}$-monopole cobordism.
The main technical difficulty in the $\mathrm{SO(3)}$-monopole program relating the Seiberg-Witten and Donaldson invariants has been to compute intersection pairings on links of strata of reducible $\mathrm{SO(3)}$ monopoles, namely the moduli spaces of Seiberg-Witten monopoles lying in lower-level strata of the Uhlenbeck compactification of the moduli space of $\mathrm{SO(3)}$ monopoles. In this monograph, the authors prove--modulo a gluing theorem which is an extension of their earlier work--that these intersection pairings can be expressed in terms of topological data and Seiberg-Witten invariants of the four-manifold.
Their proofs that the $\mathrm{SO(3)}$-monopole cobordism yields both the Superconformal Simple Type Conjecture of Moore, Marino, and Peradze and Witten's Conjecture in full generality for all closed, oriented, smooth four-manifolds with $b_1=0$ and odd $b^+\ge 3$ appear in earlier works.
Information
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Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Paperback / softback
- Pages:228 pages
- Publisher:American Mathematical Society
- Publication Date:30/01/2019
- Category:
- ISBN:9781470414214
Information
-
Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Paperback / softback
- Pages:228 pages
- Publisher:American Mathematical Society
- Publication Date:30/01/2019
- Category:
- ISBN:9781470414214
