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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

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Volume 4, Issue 1


Geometrical Decomposition of the Free Loop Space on a Manifold with Finitely Many Closed Geodesics

Thomas Morgenstern
  • Mathematisches Institut der Universität Heidelberg, Im Neuenheimer Feld 288, 69122 Heidelberg, Germany
  • Other articles by this author:
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Published Online: 2010-02-23 | DOI: https://doi.org/10.1515/GMJ.1997.65


In Morse theory an isolated degenerate critical point can be resolved into a finite number of nondegenerate critical points by perturbing the totally degenerate part of the Morse function inside the domain of a generalized Morse chart. Up to homotopy we can admit pertubations within the whole characteristic manifold. Up to homotopy type a relative CW-complex is attached, which is the product of a big relative CW-complex, representing the degenerate part, and a small cell having the dimension of the Morse index.

Key words and phrases.: Morse theory; closed geodesics; critical points; free loop space; Lusternik–Schnirelmann category

About the article

Received: 1995-04-07

Published Online: 2010-02-23

Published in Print: 1997-02-01

Citation Information: Georgian Mathematical Journal, Volume 4, Issue 1, Pages 65–80, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/GMJ.1997.65.

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