{"product_id":"9781470414214","title":"SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg-Witten Invariants","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 $b1=0$ and odd $b^+\\ge 3$ appear in earlier works.","brand":"Paul Feehan","offers":[{"title":"Default Title","offer_id":46776502681918,"sku":"9781470414214","price":0.0,"currency_code":"ZAR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4357\/7662\/products\/9781470414214_1c29bce8-6ade-4909-ba73-e63a969685f2.jpg?v=1707476968","url":"https:\/\/exclusivebooks.co.za\/products\/9781470414214","provider":"Exclusive Books Online","version":"1.0","type":"link"}