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Rétractes Absolus de Voisinage Algébriques

Cauty, Robert (2005)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 54C55, 54H25, 55M20.We introduce the class of algebraic ANRs. It is defined by replacing continuous maps by chain mappings in Lefschetz’s characterization of ANRs. To a large extent, the theory of algebraic ANRs parallels the classical theory of ANRs. Every ANR is an algebraic ANR, but the class of algebraic ANRs is much larger; the most striking difference between these classes is that every locally equiconnected metrisable space is an algebraic ANR, whereas...

Rétractes d'un espace

Mohammed El Haouari (1995)

Annales de l'institut Fourier

Notre but dans ce texte est de montrer le résultat suivant : Si X est un C.W. complexe, simplement connexe, de type fini, avec π * ( Ω X ) ⊗ ℚ finiment engendré comme algèbre de Lie, alors, à équivalence d’homotopie rationnelle près, il n’existe qu’un nombre fini de rétractes de X . L’existence d’un nombre fini de rétractes a été obtenue par L. Renner en 1990 dans le cas où H * ( X ; ℚ ) est finiment engendré en tant que ℚ -algèbre. Notre résultat élargit ainsi le cadre des espaces n’ayant, à équivalence d’homotopie rationnelle...

Retractions onto the Space of Continuous Divergence-free Vector Fields

Philippe Bouafia (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove that there does not exist a uniformly continuous retraction from the space of continuous vector fields onto the subspace of vector fields whose divergence vanishes in the distributional sense. We then generalise this result using the concept of m -charges, introduced by De Pauw, Moonens, and Pfeffer: on any subset X ⊆ ℝ n satisfying a mild geometric condition, there is no uniformly continuous representation operator for m -charges in X .

Salvetti complex, spectral sequences and cohomology of Artin groups

Filippo Callegaro (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

The aim of this short survey is to give a quick introduction to the Salvetti complex as a tool for the study of the cohomology of Artin groups. In particular we show how a spectral sequence induced by a filtration on the complex provides a very natural and useful method to study recursively the cohomology of Artin groups, simplifying many computations. In the last section some examples of applications are presented.

Second variational derivative of local variational problems and conservation laws

Marcella Palese, Ekkehart Winterroth, E. Garrone (2011)

Archivum Mathematicum

We consider cohomology defined by a system of local Lagrangian and investigate under which conditions the variational Lie derivative of associated local currents is a system of conserved currents. The answer to such a question involves Jacobi equations for the local system. Furthermore, we recall that it was shown by Krupka et al. that the invariance of a closed Helmholtz form of a dynamical form is equivalent with local variationality of the Lie derivative of the dynamical form; we remark that...

Seiberg-Witten invariants, the topological degree and wall crossing formula

Maciej Starostka (2012)

Open Mathematics

Following S. Bauer and M. Furuta we investigate finite dimensional approximations of a monopole map in the case b 1 = 0. We define a certain topological degree which is exactly equal to the Seiberg-Witten invariant. Using homotopy invariance of the topological degree a simple proof of the wall crossing formula is derived.

Currently displaying 2221 – 2240 of 3052