{"product_id":"9783030442194","title":"SpringerBriefs in Mathematics: A Minicourse on L2-Betti Numbers in Group Theory","description":"\u003ch1\u003eSpringerBriefs in Mathematics: A Minicourse on L2-Betti Numbers in Group Theory\u003c\/h1\u003e \u003ch2\u003eLöh, Clara\u003c\/h2\u003e \u003cp\u003eThis book offers a concise introduction to ergodic methods in group homology, with a particular focus on the computation of \u003ci\u003eL\u003c\/i\u003e\u003csup\u003e2\u003c\/sup\u003e-Betti numbers.\u003c\/p\u003e\u003cp\u003eGroup homology integrates group actions into homological structure. Coefficients based on probability measure preserving actions combine ergodic theory and homology. An example of such an interaction is provided by \u003ci\u003eL\u003c\/i\u003e\u003csup\u003e2\u003c\/sup\u003e-Betti numbers: these invariants can be understood in terms of group homology with coefficients related to the group von Neumann algebra, via approximation by finite index subgroups, or via dynamical systems. In this way, \u003ci\u003eL\u003c\/i\u003e\u003csup\u003e2\u003c\/sup\u003e-Betti numbers lead to orbit\/measure equivalence invariants and measured group theory helps to compute \u003ci\u003eL\u003c\/i\u003e\u003csup\u003e2\u003c\/sup\u003e-Betti numbers. Similar methods apply also to compute the rank gradient\/cost of groups as well as the simplicial volume of manifolds.\u003c\/p\u003e\u003cp\u003eThis book introduces \u003ci\u003eL\u003c\/i\u003e\u003csup\u003e2\u003c\/sup\u003e-Betti numbers of groups at an elementary level and thendevelops the ergodic point of view, emphasising the connection with approximation phenomena for homological gradient invariants of groups and spaces. The text is an extended version of the lecture notes for a minicourse at the MSRI summer graduate school “Random and arithmetic structures in topology” and thus accessible to the graduate or advanced undergraduate students. Many examples and exercises illustrate the material.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2020-03-15\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783030442194\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-030-44220-0\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 114\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":45548661440652,"sku":"9783030442194","price":62.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783030442194.jpg?v=1775785920","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783030442194","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}