{"product_id":"metacyclic-groups-d2-problem-9789811222757-new","title":"Metacyclic Groups and the D(2) Problem","description":"\u003cp\u003eThe \u003cem\u003eD\u003c\/em\u003e(2) problem is a fundamental problem in low dimensional topology. In broad terms, it asks when a three-dimensional space can be continuously deformed into a two-dimensional space without changing the essential algebraic properties of the spaces involved.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe problem is parametrized by the fundamental group of the spaces involved; that is, each group \u003cem\u003eG\u003c\/em\u003e has its own \u003cem\u003eD\u003c\/em\u003e(2) problem whose difficulty varies considerably with the individual nature of \u003cem\u003eG\u003c\/em\u003e.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis book solves the \u003cem\u003eD\u003c\/em\u003e(2) problem for a large, possibly infinite, number of finite metacyclic groups \u003cem\u003eG\u003c\/em\u003e(\u003cem\u003ep\u003c\/em\u003e, \u003cem\u003eq\u003c\/em\u003e). Prior to this the author had solved the \u003cem\u003eD\u003c\/em\u003e(2) problem for the groups \u003cem\u003eG\u003c\/em\u003e(\u003cem\u003ep\u003c\/em\u003e, 2). However, for \u003cem\u003eq\u003c\/em\u003e \u0026gt; 2, the only previously known solutions were for the groups \u003cem\u003eG\u003c\/em\u003e(7, 3), \u003cem\u003eG\u003c\/em\u003e(5, 4) and \u003cem\u003eG\u003c\/em\u003e(7, 6), all done by difficult direct calculation by two of the author's students, Jonathan Remez (2011) and Jason Vittis (2019).\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe method employed is heavily algebraic and involves precise analysis of the integral representation theory of \u003cem\u003eG\u003c\/em\u003e(\u003cem\u003ep\u003c\/em\u003e, \u003cem\u003eq\u003c\/em\u003e). Some noteworthy features are a new cancellation theory of modules (Chapters 10 and 11) and a simplified treatment (Chapters 5 and 12) of the author's theory of Swan homomorphisms.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544441061666,"sku":"9789811222757-new","price":123.85,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811222757.jpg?v=1776403873","url":"https:\/\/www.albakireads.com\/products\/metacyclic-groups-d2-problem-9789811222757-new","provider":"AlbakiReads","version":"1.0","type":"link"}