Generators of the Second Homotopy Module of Group Presentations with Applications

[摘要] The main work of this thesis starts with Chapter 2. The main problems of the thesis are the following (*) and its applications. Let P' be a subpresentation of a group presentation P and X be a set of generators of the second homotopy module pi2(P') of P'. (*) What extra elements are needed to generate pi2(P)? In Chapter 2, we study the answer about (*) when P and P' define the same group, i.e., P is a presentation obtained from P' by a sequence of Tietze transformations. And we also study the relationship between the relation modules of P and P'. In Chapter 3 and 4, we study the answers about (*) when P is (1) a graph product in

[发布机构] University:University of Glasgow

[关键词] Mathematics