{"product_id":"global-surgery-formula-for-the-casson-walker-invariant-9780691021324","title":"Global Surgery Formula for the Casson-Walker Invariant","description":"\u003cp\u003e • Author(s): Christine Lescop\u003cbr\u003e • Publisher: Princeton University Press\u003cbr\u003e • Publisher Imprint: Princeton University Press\u003cbr\u003e • BISAC: General\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book presents a new result in 3-dimensional topology. It is well known that any closed oriented 3-manifold can be obtained by surgery on a framed link in \u003ci\u003eS\u003c\/i\u003e\u003cbr\u003e 3. In \u003ci\u003eGlobal Surgery Formula for the Casson-Walker Invariant, \u003c\/i\u003e a function F of framed links in \u003ci\u003eS\u003c\/i\u003e\u003cbr\u003e 3 is described, and it is proven that F consistently defines an invariant, lamda (\u003ci\u003el\u003c\/i\u003e), of closed oriented 3-manifolds. \u003ci\u003el\u003c\/i\u003e is then expressed in terms of previously known invariants of 3-manifolds. For integral homology spheres, \u003ci\u003el\u003c\/i\u003e is the invariant introduced by Casson in 1985, which allowed him to solve old and famous questions in 3-dimensional topology. \u003ci\u003el\u003c\/i\u003e becomes simpler as the first Betti number increases. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e As an explicit function of Alexander polynomials and surgery coefficients of framed links, the function F extends in a natural way to framed links in rational homology spheres. It is proven that F describes the variation of \u003ci\u003el\u003c\/i\u003e under any surgery starting from a rational homology sphere. Thus F yields a global surgery formula for the Casson invariant.","brand":"Princeton University Press","offers":[{"title":"Paperback","offer_id":46893180584087,"sku":"9780691021324","price":8991.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780691021324.webp?v=1770314517","url":"https:\/\/atlanticbooks.com\/products\/global-surgery-formula-for-the-casson-walker-invariant-9780691021324","provider":"Atlantic Books","version":"1.0","type":"link"}