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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 

 

Classification of simple multigerms of curves in the contact space


Author: P. A. Kolgushkin
Translated by: N. Yu. Netsvetaev
Original publication: Algebra i Analiz, tom 18 (2006), nomer 2.
Journal: St. Petersburg Math. J. 18 (2007), 241-267
MSC (2000): Primary 58K40
DOI: https://doi.org/10.1090/S1061-0022-07-00950-8
Published electronically: March 19, 2007
MathSciNet review: 2244937
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Abstract: Stably simple singularities of curves (both reducible and irreducible) in the contact complex space are classified up to formal stable contact equivalence.The classification widens the one obtained by V. I. Arnold in 1999 for the simple contact space singularities that are $ RL$-equivalent to the singularity $ A_2$ (a semicubical parabola). The proofs involve the homotopy method and the Darboux-Givental theorem on contact structures.


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Additional Information

P. A. Kolgushkin
Affiliation: Mechanics and Mathematics Department, Moscow State University, Moscow 119899, Russia
Email: kolgush@mccme.ru

DOI: https://doi.org/10.1090/S1061-0022-07-00950-8
Keywords: Contact structure, contact diffeomorphism, multigerm, stably simple singularity
Received by editor(s): March 10, 2005
Published electronically: March 19, 2007
Additional Notes: Partially supported by RFBR (grant no. 01-04-00762) and by grant NSh-1972.2003.1
Article copyright: © Copyright 2007 American Mathematical Society