The E-Cohomological Conley Index, Cup-Lengths and the Arnold Conjecture on T2n

Abstract

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
• 37j10
• 53d40
• 58e05