Differential and Symplectic Topology of Knots and Curves (American Mathematical Society Translations: Series 2)

Differential and Symplectic Topology of Knots and Curves (American Mathematical Society Translations: Series 2)

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Description

This book presents a collection of papers on two related topics: topology of knots and knot-like objects (such as curves on surfaces) and topology of Legendrian knots and links in 3-dimensional contact manifolds. Featured is the work of international experts in knot theory ('quantum' knot invariants, knot invariants of finite type), in symplectic and contact topology, and in singularity theory. The interplay of diverse methods from these fields makes this volume unique in the study of Legendrian knots and knot-like objects such as wave fronts. A particularly enticing feature of the volume is its international significance. The volume successfully embodies a fine collaborative effort by worldwide experts from Belgium, France, Germany, Israel, Japan, Poland, Russia, Sweden, the U.K., and the U.S.

Contents

Contact topology, taut immersions, and Hilbert's fourth problem by J. C. Alvarez Paiva On Legendre cobordisms by E. Ferrand Vassiliev invariants of knots in $\mathbb R^3$ and in a solid torus by V. Goryunov Finite type invariants of generic immersions of $M^n$ into $\mathbb R^{2n}$ are trivial by T. Januszkiewicz and J. Swiatkowski On enumeration of unicursal curves by S. K. Lando Vassiliev invariants classify flat braids by A. B. Merkov New Whitney-type formulas for plane curves by M. Polyak Tree-like curves and their number of inflection points by B. Shapiro Geometry of exact transverse line fields and projective billiards by S. Tabachnikov Shadows of wave fronts and Arnold-Bennequin type invariants of fronts on surfaces and orbifolds by V. Tchernov A unified approach to the four vertex theorems. I by M. Umehara A unified approach to the four vertex theorems. II by G. Thorbergsson and M. Umehara Topology of two-connected graphs and homology of spaces of knots by V. A. Vassiliev.

Product Details

  • ISBN13: 9780821813546
  • Format: Hardback
  • Number Of Pages: 286
  • ID: 9780821813546
  • ISBN10: 0821813544

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