American Mathematical Society TranslationsSeries 2 Advances in the Mathematical Sciences 1999; 286 pp; hardcover Volume: 190 ISBN10: 0821813544 ISBN13: 9780821813546 List Price: US$114 Member Price: US$91.20 Order Code: TRANS2/190
 This book presents a collection of papers on two related topics: topology of knots and knotlike objects (such as curves on surfaces) and topology of Legendrian knots and links in 3dimensional 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 knotlike 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. Readership Graduate students and research mathematicians working in manifolds and cell complexes. Table of Contents  J. C. Álvarez Paiva  Contact topology, taut immersions, and Hilbert's fourth problem
 E. Ferrand  On Legendre cobordisms
 V. Goryunov  Vassiliev invariants of knots in \(\mathbb R^3\) and in a solid torus
 T. Januszkiewicz and J. Świątkowski  Finite type invariants of generic immersions of \(M^n\) into \(\mathbb R^{2n}\) are trivial
 S. K. Lando  On enumeration of unicursal curves
 A. B. Merkov  Vassiliev invariants classify flat braids
 M. Polyak  New Whitneytype formulas for plane curves
 B. Shapiro  Treelike curves and their number of inflection points
 S. Tabachnikov  Geometry of exact transverse line fields and projective billiards
 V. Tchernov  Shadows of wave fronts and ArnoldBennequin type invariants of fronts on surfaces and orbifolds
 M. Umehara  A unified approach to the four vertex theorems. I
 G. Thorbergsson and M. Umehara  A unified approach to the four vertex theorems. II
 V. A. Vassiliev  Topology of twoconnected graphs and homology of spaces of knots
