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Advanced Nonlinear Studies

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The E-Cohomological Conley Index, Cup-Lengths and the Arnold Conjecture on T 2n

Maciej Starostka
  • Corresponding author
  • Ruhr-Universität Bochum, Bochum, Germany; and Gdańsk University of Technology, Gdańsk, Polen
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/ Nils Waterstraat
  • Institut für Mathematik, Naturwissenschaftliche Fakultät II, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle (Saale), Germany
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Published Online: 2019-04-16 | DOI: https://doi.org/10.1515/ans-2019-2044


We show that the E-cohomological Conley index, that was introduced by the first author recently, has a natural module structure. This yields a new cup-length and a lower bound for the number of critical points of functionals on Hilbert spaces. When applied to the setting of the Arnold conjecture, this paves the way to a short proof on tori, where it was first shown by C. Conley and E. Zehnder in 1983.

Keywords: Critical Points; Arnold Conjecture

MSC 2010: 37J10; 53D40; 58E05


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About the article

Received: 2018-03-12

Revised: 2019-01-18

Accepted: 2019-03-13

Published Online: 2019-04-16

Maciej Starostka was supported by the grants Preludium9 of the National Science Centre, no. 2015/17/N/ST1/02527 as well as BEETHOVEN2 of the National Science Centre, Poland, no. 2016/23/G/ST1/ 04081. Nils Waterstraat was supported by the grant BEETHOVEN2 of the National Science Centre, Poland, no. 2016/23/G/ST1/04081.

Citation Information: Advanced Nonlinear Studies, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365, DOI: https://doi.org/10.1515/ans-2019-2044.

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