{"product_id":"9789811678370","title":"SpringerBriefs in Mathematical Physics: Wall-Crossing and Refined Invariants","description":"\u003ch1\u003eSpringerBriefs in Mathematical Physics: Wall-Crossing and Refined Invariants\u003c\/h1\u003e \u003ch2\u003eToda, Yukinobu\u003c\/h2\u003e \u003cp\u003eThis book is an exposition of recent progress on the Donaldson–Thomas (DT) theory. The DT invariant was introduced by R. Thomas in 1998 as a virtual counting of stable coherent sheaves on Calabi–Yau 3-folds. Later, it turned out that the DT invariants have many interesting properties and appear in several contexts such as the Gromov–Witten\/Donaldson–Thomas conjecture on curve-counting theories, wall-crossing in derived categories with respect to Bridgeland stability conditions, BPS state counting in string theory, and others. \u003c\/p\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003eRecently, a deeper structure of the moduli spaces of coherent sheaves on Calabi–Yau 3-folds was found through derived algebraic geometry. These moduli spaces admit shifted symplectic structures and the associated d-critical structures, which lead to refined versions of DT invariants such as cohomological DT invariants. The idea of cohomological DT invariants led to a mathematical definition of the Gopakumar–Vafa invariant, which was firstproposed by Gopakumar–Vafa in 1998, but its precise mathematical definition has not been available until recently.\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003eThis book surveys the recent progress on DT invariants and related topics, with a focus on applications to curve-counting theories.\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2021-12-16\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9789811678370\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-981-16-7838-7\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 104\u003c\/p\u003e ","brand":"Springer Nature Singapore","offers":[{"title":"Default Title","offer_id":46547629244556,"sku":"9789811678370","price":62.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9789811678370.jpg?v=1775835745","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9789811678370","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}