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St. Petersburg Mathematical Journal

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

 
 

 

Oriented area is a perfect Morse function


Author: G. Panina
Translated by: the author
Original publication: Algebra i Analiz, tom 29 (2017), nomer 3.
Journal: St. Petersburg Math. J. 29 (2018), 469-474
MSC (2010): Primary 52R70, 52B99
DOI: https://doi.org/10.1090/spmj/1503
Published electronically: March 30, 2018
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Abstract | References | Similar Articles | Additional Information

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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Additional 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

DOI: https://doi.org/10.1090/spmj/1503
Keywords: Morse index, polygonal linkage, flexible polygon.
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)
Article copyright: © Copyright 2018 American Mathematical Society

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