Polo Sport  Polo Club  Polo ponies  Players Equipment  The field  Notable players  Handicap players Classical And Involutive Invariants Of Krull Domains RRP $27.99 Just suppose, for a moment, that all rings of integers in algebraic number fields were unique factorization domains, then it would be fairly easy to produce a proof of Fermat's Last Theorem, fitting, say, in the margin of this page. Unfortunately however, rings of integers are not that nice in general, so that, for centuries, mathÂ ematicians had to search for alternative proofs, a quest which culminated finally in Wiles' marvelous results  but this is history. The fact remains that modern algebraic number theory really started off with inÂ vestigating the problem which rings of integers actually are unique factorization domains. The best approach to this question is, of course, through the general theÂ ory of Dedekind rings, using the full power of their class group, whose vanishing is, by its very definition, equivalent to the unique factorization property. Using the fact that a Dedekind ring is essentially just a onedimensional global version of discrete valuation rings, one easily verifies that the class group of a Dedekind ring coincides with its Picard group, thus making it into a nice, functorial invariant, which may be studied and calculated through algebraic, geometric and co homological methods. In view of the success of the use of the class group within the framework of Dedekind rings, one may wonder whether it may be applied in other contexts as well. However, for more general rings, even the definition of the class group itself causes problems. RRP $372.99 This book provides an extensive and selfcontained presentation of quantum and related invariants of knots and 3manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the KnizhnikZamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become wellorganized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3manifolds are discussed. The ChernSimons field theory and the WessZuminoWitten model are described as the physical background of the invariants. RRP $354.99 In algebraic topology some classical invariants  such as Betti numbers and Reidemeister torsion  are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to noncompact spaces and infinite groups. These new L2invariants contain very interesting and novel information and can be applied to problems arising in topology, KTheory, differential geometry, noncommutative geometry and spectral theory. It is particularly these interactions with different fields that make L2invariants very powerful and exciting. The book presents a comprehensive introduction to this area of research, as well as its most recent results and developments. It is written in a way which enables the reader to pick out a favourite topic and to find the result she or he is interested in quickly and without being forced to go through other material. Search
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