Polo Sport  Polo Club  Polo ponies  Players Equipment  The field  Notable players  Handicap players 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. Flow Lines And Algebraic Invariants In Contact Form Geometry RRP $464.99 This text features a careful treatment of flow lines and algebraic invariants in contact form geometry, a vast area of research connected to symplectic field theory, pseudoholomorphic curves, and GromovWitten invariants (contact homology). In particular, it develops a novel algebraic tool in this field: rooted in the concept of critical points at infinity, the new algebraic invariants defined here are useful in the investigation of contact structures and Reeb vector fields. The book opens with a review of prior results and then proceeds through an examination of variational problems, nonFredholm behavior, true and false critical points at infinity, and topological implications. An increasing convergence with regular and singular Yamabetype problems is discussed, and the intersection between contact form and Riemannian geometry is emphasized. Rich in open problems and full, detailed proofs, this work lays the foundation for new avenues of study in contact form geometry and will benefit graduate students and researchers. 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. Search
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