Contemporary Mathematics 1999; 249 pp; softcover Volume: 233 ISBN10: 0821808842 ISBN13: 9780821808849 List Price: US$65 Member Price: US$52 Order Code: CONM/233
 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 3spheres, 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 2dimensional CWcomplexes
 A. Kawauchi  The quadratic form of a link
 H. Murakami  Quantum \(SU(2)\)invariants of threemanifolds associated with the trivial first cohomology class modulo two
 G. Masbaum  An element of infinite order in TQFTrepresentations of mapping class groups
 T. Ohtsuki  The perturbative \(SO(3)\) invariant of homology circles
 A. S. Cattaneo  Configuration space integrals and invariants for 3manifolds and knots
 H. R. Morton  The multivariable Alexander polynomial for a closed braid
 K. Kobayashi  Boundary links and hsplit links
 K. Habiro, T. Kanenobu, and A. Shima  Finite type invariants of ribbon 2knots
 S. Kamada  Arrangement of Markov moves for 2dimensional 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
