Abstract
Consider the infinite-dimensional dynamical system provided by the (forward) heat semi-flow on the loop space of a closed Riemannian manifold M. We use the recently discovered backward \( \lambda \)-Lemma and elements of Conley theory to construct a Morse filtration of the loop space whose cellular filtration complex represents the Morse complex associated to the downward L 2-gradient of the classical action functional. This paper is a survey. Details and proofs will be given in [6].
Mathematics Subject Classification (2010). 58-02 (Primary); 58B05, 35K91 (Secondary).
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References
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J. Weber, Stable foliations and the homology of the loop space. In preparation.
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Dedicated to Bernhard Ruf on the occasion of his 60th birthday
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Weber, J. (2014). The Backward \( \lambda \)-Lemma and Morse Filtrations. In: de Figueiredo, D., do Ó, J., Tomei, C. (eds) Analysis and Topology in Nonlinear Differential Equations. Progress in Nonlinear Differential Equations and Their Applications, vol 85. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-04214-5_27
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DOI: https://doi.org/10.1007/978-3-319-04214-5_27
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Publisher Name: Birkhäuser, Cham
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