{"product_id":"9783030282967","title":"Lecture Notes in Mathematics","description":"\u003ch1\u003eLecture Notes in Mathematics\u003c\/h1\u003e \u003ch2\u003eKammeyer, Holger\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cdiv\u003eThis book introduces the reader to the most important concepts and problems in the field of ℓ²-invariants. After some foundational material on group von Neumann algebras, ℓ²-Betti numbers are defined and their use is illustrated by several examples. The text continues with Atiyah's question on possible values of ℓ²-Betti numbers and the relation to Kaplansky's zero divisor conjecture. The general definition of ℓ²-Betti numbers allows for applications in group theory. A whole chapter is dedicated to Lück's approximation theorem and its generalizations. The final chapter deals with ℓ²-torsion, twisted variants and the conjectures relating them to torsion growth in homology.\u003c\/div\u003e\u003cdiv\u003e \u003c\/div\u003e\u003cdiv\u003eThe text provides a self-contained treatment that constructs the required specialized concepts from scratch. It comes with numerous exercises and examples, so that both graduate students and researchers will find it useful for self-study or as a basis for an advanced lecture course.\u003c\/div\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2019-10-31\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783030282967\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-030-28297-4\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 183\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":45369835847820,"sku":"9783030282967","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783030282967.jpg?v=1775675708","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783030282967","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}