A geometric Morse-Novikov complex with infinite series coefficients

François Laudenbach; Carlos Moraga Ferrandiz

doi:10.1016/j.crma.2018.09.008

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arXiv · 1811.11428

A geometric Morse-Novikov complex with infinite series coefficients

François Laudenbach·Carlos Moraga Ferrandiz

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Abstract

Let M be a closed n-dimensional manifold, n > 2, whose first real cohomology group H 1 (M ; R) is non-zero. We present a general method for constructing a Morse 1-form $\alpha$ on M , closed but non-exact, and a pseudo-gradient X such that the differential $\partial$ X of the Novikov complex of the pair ($\alpha$, X) has at least one incidence coefficient which is an infinite series. This is an application of our previous study of the homoclinic bifurcation of pseudo-gradients of multivalued Morse functions.

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François Laudenbach, Carlos Moraga Ferrandiz. 2018-11-28. A geometric Morse-Novikov complex with infinite series coefficients. https://doi.org/10.1016/j.crma.2018.09.008

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