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Metacyclic Groups And The D(2) Problem (Hardcover)
Loot Price: R3,230
Discovery Miles 32 300
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Metacyclic Groups And The D(2) Problem (Hardcover)
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The D(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.The problem is parametrized by the fundamental group of
the spaces involved; that is, each group G has its own D(2) problem
whose difficulty varies considerably with the individual nature of
G.This book solves the D(2) problem for a large, possibly infinite,
number of finite metacyclic groups G(p, q). Prior to this the
author had solved the D(2) problem for the groups G(p, 2). However,
for q > 2, the only previously known solutions were for the
groups G(7, 3), G(5, 4) and G(7, 6), all done by difficult direct
calculation by two of the author's students, Jonathan Remez (2011)
and Jason Vittis (2019).The method employed is heavily algebraic
and involves precise analysis of the integral representation theory
of G(p, q). 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.
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