{"product_id":"metacyclic-groups-and-the-d2-johnson-francis-e-a-9789811222757","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\u003cbr\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\u003cbr\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\u003cbr\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\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Johnson Francis E a\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 9811222754\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9789811222757\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e World Scientific Publishing Company\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 01\/14\/2021\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 372\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.47lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.00h x 6.00w x 0.88d","brand":"Johnson Francis E a","offers":[{"title":"Hardcover","offer_id":48446702780671,"sku":"9789811222757","price":118.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_0f733bf5-6c68-4726-98b8-2894b6a03335.jpg?v=1777226391","url":"https:\/\/www.whiterainbookhouse.com\/products\/metacyclic-groups-and-the-d2-johnson-francis-e-a-9789811222757","provider":"WR Book House","version":"1.0","type":"link"}