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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

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

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

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Oriented area is a perfect Morse function
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by G. Panina
Translated by: the author
St. Petersburg Math. J. 29 (2018), 469-474
DOI: https://doi.org/10.1090/spmj/1503
Published electronically: March 30, 2018
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Abstract:

An appropriate generalization of the oriented area function is a perfect Morse function on the space of three-dimensional configurations of an equilateral polygonal linkage with odd number of edges. Therefore, the cyclic equilateral polygons (which appear as Morse points) can be viewed as independent generators of the homology groups of the (decorated) configuration space.
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Bibliographic Information
  • G. Panina
  • Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia; St. Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg 199034, Russia
  • Email: gaiane-panina@rambler.ru
  • Received by editor(s): July 11, 2016
  • Published electronically: March 30, 2018
  • Additional Notes: Supported by the Russian Science Foundation (grant no. 16-11-10039)
  • © Copyright 2018 American Mathematical Society
  • Journal: St. Petersburg Math. J. 29 (2018), 469-474
  • MSC (2010): Primary 52R70, 52B99
  • DOI: https://doi.org/10.1090/spmj/1503
  • MathSciNet review: 3708859