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Book DetailsContemporary MathematicsVolume: 233; 1999; 249 ppMSC: Primary 57
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.
ReadershipGraduate students and research mathematicians working in manifolds and cell complexes; physicists, chemists, and biologists working in genetics and molecular biology.
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Table of Contents
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Articles
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Valentin Poénaru — $\pi ^\infty _1$ and infinite simple homotopy type in dimension $3$ [ MR 1701672 ]
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Louis Funar — Cubulations mod bubble moves [ MR 1701673 ]
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Ivelina Bobtcheva and Frank Quinn — Numerical presentations of tortile categories [ MR 1701674 ]
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Ivelina Bobtcheva — On Quinn’s invariants of $2$-dimensional CW-complexes [ MR 1701675 ]
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Akio Kawauchi — The quadratic form of a link [ MR 1701676 ]
-
Hitoshi Murakami — Quantum ${\rm SU}(2)$-invariants of three-manifolds associated with the trivial first cohomology class modulo two [ MR 1701677 ]
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Gregor Masbaum — An element of infinite order in TQFT-representations of mapping class groups [ MR 1701678 ]
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Tomotada Ohtsuki — The perturbative ${\rm SO}(3)$ invariant of homology circles [ MR 1701679 ]
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Alberto S. Cattaneo — Configuration space integrals and invariants for $3$-manifolds and knots [ MR 1701680 ]
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H. R. Morton — The multivariable Alexander polynomial for a closed braid [ MR 1701681 ]
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Kazuaki Kobayashi — Boundary links and $h$-split links [ MR 1701682 ]
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Kazuo Habiro, Taizo Kanenobu and Akiko Shima — Finite type invariants of ribbon $2$-knots [ MR 1701683 ]
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Seiichi Kamada — Arrangement of Markov moves for $2$-dimensional braids [ MR 1701684 ]
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Paweł Traczyk — A criterion for signed unknotting number [ MR 1701685 ]
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H. Nencka — On some extensions of Artin’s braid relations [ MR 1701686 ]
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Jun O’Hara — Asymptotic behavior of energy of polygonal knots [ MR 1701687 ]
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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.
Graduate students and research mathematicians working in manifolds and cell complexes; physicists, chemists, and biologists working in genetics and molecular biology.
-
Articles
-
Valentin Poénaru — $\pi ^\infty _1$ and infinite simple homotopy type in dimension $3$ [ MR 1701672 ]
-
Louis Funar — Cubulations mod bubble moves [ MR 1701673 ]
-
Ivelina Bobtcheva and Frank Quinn — Numerical presentations of tortile categories [ MR 1701674 ]
-
Ivelina Bobtcheva — On Quinn’s invariants of $2$-dimensional CW-complexes [ MR 1701675 ]
-
Akio Kawauchi — The quadratic form of a link [ MR 1701676 ]
-
Hitoshi Murakami — Quantum ${\rm SU}(2)$-invariants of three-manifolds associated with the trivial first cohomology class modulo two [ MR 1701677 ]
-
Gregor Masbaum — An element of infinite order in TQFT-representations of mapping class groups [ MR 1701678 ]
-
Tomotada Ohtsuki — The perturbative ${\rm SO}(3)$ invariant of homology circles [ MR 1701679 ]
-
Alberto S. Cattaneo — Configuration space integrals and invariants for $3$-manifolds and knots [ MR 1701680 ]
-
H. R. Morton — The multivariable Alexander polynomial for a closed braid [ MR 1701681 ]
-
Kazuaki Kobayashi — Boundary links and $h$-split links [ MR 1701682 ]
-
Kazuo Habiro, Taizo Kanenobu and Akiko Shima — Finite type invariants of ribbon $2$-knots [ MR 1701683 ]
-
Seiichi Kamada — Arrangement of Markov moves for $2$-dimensional braids [ MR 1701684 ]
-
Paweł Traczyk — A criterion for signed unknotting number [ MR 1701685 ]
-
H. Nencka — On some extensions of Artin’s braid relations [ MR 1701686 ]
-
Jun O’Hara — Asymptotic behavior of energy of polygonal knots [ MR 1701687 ]
