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Search Results: 1 - 10 of 2359 matches for " Francois Laudenbach "
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On the codimension-one foliation theorem of W. Thurston
Francois Laudenbach
Mathematics , 2006,
Abstract: This article has been withdrawn due to a mistake which is explained in version 2.
A Note on the Chas-Sullivan product
Francois Laudenbach
Mathematics , 2009,
Abstract: We give a finite dimensional approach to the Chas-Sullivan product on the free loop space of a manifold, orientable or not.
On an article by S. A. Barannikov
Francois Laudenbach
Mathematics , 2015,
Abstract: Given a Morse function f on a closed manifold M with distinct critical values, and given a field F, there is a canonical complex, called the Morse-Barannikov complex, which is equivalent to any Morse complex associated with f and whose form is simple. In particular, the homology of M with coefficients in F is immediately readable on this complex. The bifurcation theory of this complex in a generic one-parameter family of functions will be investigated. Applications to the boundary manifolds will be given.
Positive Legendrian regular homotopies
Francois Laudenbach
Mathematics , 2008,
Abstract: In contrast with what happens for Legendrian embeddings, there always exist positive loops of Legendrian immersions.
A proof of Reidemeister-Singer's theorem by Cerf's methods
Francois Laudenbach
Mathematics , 2012,
Abstract: Heegaard splittings and Heegaard diagrams of a closed 3-manifold M are translated into the language of Morse functions with Morse-Smale pseudo-gradients defined on M. We make use in a very simple setting of techniques which Jean Cerf developed for solving a famous pseudo-isotopy problem. In passing, we show how to cancel the supernumerary local extrema in a generic path of functions when dim M>2. The main tool that we introduce is an elementary swallow tail lemma which could be useful elsewhere.
A Morse complex on manifolds with boundary
Francois Laudenbach
Mathematics , 2010,
Abstract: Given a compact smooth manifold $M$ with non-empty boundary and a Morse function, a pseudo-gradient Morse-Smale vector field adapted to the boundary allows one to build a Morse complex whose homology is isomorphic to the (absolute or relative to the boundary) homology of $M$ with integer coefficients. Our approach simplifies other methods which have been discussed in more specific geometric settings.
A proof of Morse's theorem about the cancellation of critical points
Francois Laudenbach
Mathematics , 2013,
Abstract: In this note, we give a proof of the famous theorem of M. Morse dealing with the cancellation of a pair of non-degenerate critical points of a smooth function. Our proof consists of a reduction to the one-dimensional case where the question becomes easy to answer.
Haefliger structures and symplectic/contact structures
Francois Laudenbach,Gael Meigniez
Mathematics , 2015,
Abstract: For some geometries including symplectic and contact structures on an n-dimensional manifold, we introduce a two-step approach to Gromov's h-principle. From formal geometric data, the first step builds a transversely geometric Haefliger structure of codimension n. This step works on all manifolds, even closed. The second step, which works only on open manifolds and for all geometries, regularizes the intermediate Haefliger structure and produces a genuine geometric structure. Both steps admit relative parametric versions. The proofs borrow ideas from W. Thurston, like jiggling and inflation. Actually, we are using a more primitive jiggling due to R. Thom.
Regularization of Gamma_1-structures in dimension 3
Francois Laudenbach,Ga?l Meigniez
Mathematics , 2009,
Abstract: For $\Gamma_1$-structures on 3-manifolds, we give a very simple proof of Thurston's regularization theorem, first proved in \cite{thurston}, without using Mather's homology equivalence. Moreover, in the co-orientable case, the resulting foliation can be chosen of a precise kind, namely an "open book foliation modified by suspension." There is also a model in the non co-orientable case.
Haefliger's codimension-one singular foliations, open books and twisted open books in dimension 3
Francois Laudenbach,Gael Gael Meigniez
Mathematics , 2011,
Abstract: We consider singular foliations of codimension one on 3-manifolds, in the sense defined by A. Haefliger as being Gamma_1-structures. We prove that under the obvious linear embedding condition, they are Gamma_1-homotopic to a regular foliation carried by an open book or a twisted open book. The latter concept is introduced for this aim. Our result holds true in every regularity C^r, r at least 1. In particular, in dimension 3, this gives a very simple proof of Thurston's 1976 regularization theorem without using Mather's homology equivalence.
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