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Shadows of Legendrian Links and J +-Theory of Curves

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Singularities

Part of the book series: Progress in Mathematics ((PM,volume 162))

Abstract

We introduce invariants of 2-component fronts similar to Arnold’s [1] invariants J ± following approach of Viro [22] and generalize Viro’s formulae to invariants of 1 and 2-component 0-homologous fronts on surfaces of non-zero Euler characteristic. We modify Turaev’s construction [19] of link shadows and define shadows of Legendrian links in ST* S 2. This enables us to relate integral formulae for J +-type invariants of fronts to Turaev’s [19] shadow formulae for linking and self-linking numbers applied to Legendrian shadows. Other applications of Legendrian shadows, e.g. quantum J +-type invariants of fronts are discussed.

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Author information

Authors and Affiliations

  1. IHES Le Bois-Marie, 35 Route de Chartres, F91440, Bures-sur-Yvette, France

    Michael Polyak

  2. Dept. of Mathematics, Hebrew University of Jerusalem, Givat Ram, Jerusalem, 91904, Israel

    Michael Polyak

Authors
  1. Michael Polyak
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Editor information

Editors and Affiliations

  1. Department of Geometry and Topology, Steklov Mathematical Institute, 8, Gubkina Stree, 117966, Moscow GSP-1, Russia

    V. I. Arnold

  2. CEREMADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, Postfach 3049, F-75775, Paris Cedex 16e, France

    V. I. Arnold

  3. Fachbereich Mathematik, Universität Kaiserslautern, D-67653, Kaiserslautern, Germany

    G.-M. Greuel

  4. Subfaculteit Wiskunde, Katholieke Universiteit Nijmegen Toernooiveld, NL-6525 ED, Nijmegen, The Netherlands

    J. H. M. Steenbrink

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© 1998 Springer Basel AG

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Polyak, M. (1998). Shadows of Legendrian Links and J +-Theory of Curves. In: Arnold, V.I., Greuel, GM., Steenbrink, J.H.M. (eds) Singularities. Progress in Mathematics, vol 162. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8770-0_21

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  • DOI: https://doi.org/10.1007/978-3-0348-8770-0_21

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9767-9

  • Online ISBN: 978-3-0348-8770-0

  • eBook Packages: Springer Book Archive

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