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Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21970

Tchernov, V (2002). Arnold-type invariants of wave fronts on surfaces. Topology, 41(1):1-45.

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Abstract

Recently, Arnold's St and J± invariants of generic planar curves have been generalized to the case of generic planar wave fronts. We generalize these invariants to the case of wave fronts on an arbitrary surface F. All invariants satisfying the axioms which naturally generalize the axioms used by Arnold are explicitly described. We also give an explicit formula for the finest order one J+-type invariant of fronts on an orientable surface F≠S2. We obtain necessary and sufficient conditions for an invariant of nongeneric fronts with one nongeneric singular point to be the Vassiliev-type derivative of an invariant of generic fronts. As a byproduct, we calculate all homotopy groups of the space of Legendrian immersions of S1 into the spherical cotangent bundle of a surface.

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
DDC:510 Mathematics
Language:English
Date:2002
Deposited On:29 Nov 2010 17:27
Last Modified:30 Dec 2013 20:23
Publisher:Elsevier
ISSN:0040-9383
Publisher DOI:10.1016/S0040-9383(00)00013-6
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1017.57006
http://www.ams.org/mathscinet-getitem?mr=1871239
Citations:Web of Science®. Times Cited: 3
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