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Low Dimensional Topology
Edited by: Hanna Nencka, University of Madeira, Funchal, Madeira, Portugal
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Contemporary Mathematics
1999; 249 pp; softcover
Volume: 233
ISBN-10: 0-8218-0884-2
ISBN-13: 978-0-8218-0884-9
List Price: US$65
Member Price: US$52
Order Code: CONM/233
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This volume presents the proceedings from the conference on low dimensional topology held at the University of Madeira (Portugal). The event was attended by leading scientists in the field from the U.S., Asia, and Europe.

The book has two main parts. The first is devoted to the Poincaré conjecture, characterizations of \(PL\)-manifolds, covering quadratic forms of links and to categories in low dimensional topology that appear in connection with conformal and quantum field theory. The second part of the volume covers topological quantum field theory and polynomial invariants for rational homology 3-spheres, derived from the quantum \(SU(2)\)-invariants associated with the first cohomology class modulo two, knot theory, and braid groups. This collection reflects development and progress in the field and presents interesting and new results.

Readership

Graduate students and research mathematicians working in manifolds and cell complexes; physicists, chemists, and biologists working in genetics and molecular biology.

Table of Contents

  • V. Poénaru -- \(\pi^\infty_1\) and infinite simple homotopy type in dimension 3
  • L. Funar -- Cubulations mod bubble moves
  • I. Bobtcheva and F. Quinn -- Numerical presentations of tortile categories
  • I. Bobtcheva -- On Quinn's invariants of 2-dimensional CW-complexes
  • A. Kawauchi -- The quadratic form of a link
  • H. Murakami -- Quantum \(SU(2)\)-invariants of three-manifolds associated with the trivial first cohomology class modulo two
  • G. Masbaum -- An element of infinite order in TQFT-representations of mapping class groups
  • T. Ohtsuki -- The perturbative \(SO(3)\) invariant of homology circles
  • A. S. Cattaneo -- Configuration space integrals and invariants for 3-manifolds and knots
  • H. R. Morton -- The multivariable Alexander polynomial for a closed braid
  • K. Kobayashi -- Boundary links and h-split links
  • K. Habiro, T. Kanenobu, and A. Shima -- Finite type invariants of ribbon 2-knots
  • S. Kamada -- Arrangement of Markov moves for 2-dimensional braids
  • P. Traczyk -- A criterion for signed unknotting number
  • H. Nencka -- On some extensions of Artin's braid relations
  • J. O'Hara -- Asymptotic behavior of energy of polygonal knots
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