70 research outputs found
A topological join construction and the Toda system on compact surfaces of arbitrary genus
No full textWe consider a Toda system of Liouville equations defined on a compact surface
which arises as a model for non-abelian Chern-Simons vortices. For the first
time the range of parameters , , is studied with a variational approach
on surfaces with arbitrary genus. We provide a general existence result by
means of a new improved Moser-Trudinger type inequality and introducing a
topological join construction in order to describe the interaction of the two
components
Homological splitting methods in topology and geometry
No full textÉtant donné un espace topologique filtré X, nous donnons des critères explicites pour pouvoir scinder sa filtratlon associée par rapport à une théorie généralisée de l'homologie, Nous reproduisons ainsi et de manière unifiée les scindements classiques de Snaith (pour les espaces de lacets), de Steenrod (pour les produits symétriques) et multiples autres exemples. Ces scindements sont de grande utilité en topologie algébrique. Nous étendons également le scindement de Steenrod aux espaces de permutations et puis donnons plusieurs nouvelles applications de nos techniques de scindements aux espaces de confïgurations, aux produits polyèdraux, aux fonctions rationnelles et aux espaces de « particules ».Given a fïltered space X, we provide useful criteria to split the associated filtration on X with respect to a generalized homology theory. We recover in a unifïed way the classlcal splittings of Snaith (for iterated loop spaces), of Steenrod (for the symmetric products) and mam others (contïguratlon spaces, classifying spaces). We extend the splitting of Steenrod to permutation products and to other situations. We then apply our techniques to exhibit splittings for polyhedral spaces, rational functions and "particle spaces
Formal barycenter spaces with weights: the Euler characteristic
No full textWe compute the Euler characteristic with compact supports of the formal barycenter spaces with weights of some locally compact spaces, connected or not. This reduces to the topological Euler characteristic when the weights of the singular points are less than one. As foresighted by Andrea Malchiodi, our formula is related to the Leray-Schauder degree for mean field equations on a compact Riemann surface obtained by C.C. Chen and C.S.\ Lin
Configuration Spaces of Points: A User's Guide
No full textThis extensive survey is an invited contribution to the Encyclopedia of
Mathematical Physics, 2nd edition. It covers both classical and more modern
aspects of configuration spaces of points on a "ground space" . Most results
pertain to a manifold. Configuration spaces of points have become so
omnipresent in so many areas of mathematics, physics, and even the applied
sciences, that a survey can only cover a selection of topics. We review key
ideas, constructions, and results.Comment: 50 pages. Comments and feedback are quite welcom
Topological reconstruction of compact supports of dependent stationary random variables
No full textInternational audienceIn this paper we extend results on reconstruction of probabilistic supports of random i.i.d variables to supports of dependent stationary -valued random variables. All supports are assumed to be compact of positive reach in Euclidean space. Our main results involve the study of the convergence in the Hausdorff sense of a cloud of stationary dependent random vectors to their common support. A novel topological reconstruction result is stated, and a number of illustrative examples are presented. The example of the Möbius Markov chain on the circle is treated at the end with simulations
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