EuDML | Browse

Si definisce il gruppo di $i$ —omotopia di un singolo modulo e si introduce la nozione di equivalenza $i$ -omotopica debole. Sotto determinate condizioni per l'anello di base $\Lambda$ oppure per i moduli considerati, le equivalenze $i$ -omotopiche deboli coincidono con le equivalenze $i$ -omotopiche (forti).

Opérades cellulaires et espaces de lacets itérés

Clemens Berger (1996)

Annales de l'institut Fourier

L’espace des configurations de $p$ points distincts de $R^{\infty}$ admet une filtration naturelle qui est induite par les inclusions des $R^{n}$ dans $R^{\infty}$ . Nous caractérisons le type d’homotopie de cette filtration par les propriétés combinatoires d’une structure cellulaire sous-jacente, étroitement liée à la théorie des $E_{n}$ -opérades de May. Cela donne une approche unifiée des différents modèles combinatoires d’espaces de lacets itérés et redémontre les théorèmes d’approximation de Milgram, Smith et Kashiwabara.

Postnikov invariants of H-spaces

Dominique Arlettaz, Nicole Pointet-Tischler (1999)

Fundamenta Mathematicae

It is known that the order of all Postnikov k-invariants of an H-space of finite type is finite. This paper establishes the finiteness of the order of the k-invariants $k^{m + 1} (X)$ of X in dimensions m ≤ 2n if X is an (n-1)-connected H-space which is not necessarily of finite type (n ≥ 1). Similar results hold more generally for higher k-invariants if X is an iterated loop space. Moreover, we provide in all cases explicit universal upper bounds for the order of the k-invariants of X.

Product and other fine structure in polynomial resolutions of mapping spaces.

Ahearn, Stephen T., Kuhn, Nicholas J. (2002)

Algebraic & Geometric Topology

Product splittings for p-compact groups

W. Dwyer, C. Wilkerson (1995)

Fundamenta Mathematicae

We show that a connected p-compact group with a trivial center is equivalent to a product of simple p-compact groups. More generally, we show that product splittings of any connected p-compact group correspond bijectively to algebraic splittings of the fundamental group of the maximal torus as a module over the Weyl group. These are analogues for p-compact groups of well-known theorems about compact Lie groups.

Rational BV-algebra in string topology

Yves Félix, Jean-Claude Thomas (2008)

Bulletin de la Société Mathématique de France

Let $M$ be a 1-connected closed manifold of dimension $m$ and $L M$ be the space of free loops on $M$ . M.Chas and D.Sullivan defined a structure of BV-algebra on the singular homology of $L M$ , $H_{*} (L M; k)$ . When the ring of coefficients is a field of characteristic zero, we prove that there exists a BV-algebra structure on the Hochschild cohomology $H H^{*} (C^{*} (M); C^{*} (M))$ which extends the canonical structure of Gerstenhaber algebra. We construct then an isomorphism of BV-algebras between $H H^{*} (C^{*} (M); C^{*} (M))$ and the shifted homology $H_{* + m} (L M; k)$ . We also prove that the...

Rational string topology

Yves Félix, Jean-Claude Thomas, Micheline Vigué-Poirrier (2007)

Journal of the European Mathematical Society

We use the computational power of rational homotopy theory to provide an explicit cochain model for the loop product and the string bracket of a simply connected closed manifold $M$ . We prove that the loop homology of $M$ is isomorphic to the Hochschild cohomology of the cochain algebra $C^{*} (M)$ with coefficients in $C^{*} (M)$ . Some explicit computations of the loop product and the string bracket are given.

Some homotopy theoretical questions arising in Nielsen coincidence theory

Ulrich Koschorke (2009)

Banach Center Publications

Basic examples show that coincidence theory is intimately related to central subjects of differential topology and homotopy theory such as Kervaire invariants and divisibility properties of Whitehead products and of Hopf invariants. We recall some recent results and ask a few questions which seem to be important for a more comprehensive understanding.

Spaces of polynomials with roots of bounded multiplicity

M. Guest, A. Kozlowski, K. Yamaguchi (1999)

Fundamenta Mathematicae

We describe an alternative approach to some results of Vassiliev ([Va1]) on spaces of polynomials, by applying the "scanning method" used by Segal ([Se2]) in his investigation of spaces of rational functions. We explain how these two approaches are related by the Smale-Hirsch Principle or the h-Principle of Gromov. We obtain several generalizations, which may be of interest in their own right.

Currently displaying 61 – 80 of 106

Previous Page 4 Next

Displaying 61 – 80 of 106

On the cohomology ring of the free loop space of a wedge of spheres.

On the construction of the Kan loop group.

On the fundamental group of a mapping space. An example

On the geometry of free loop spaces.

On the Homology of Non-Connected Monoids and Their Associated Groups

On the homotopy groups of a finite dimensional space.

On weak $i$ -homotopy equivalences of modules

Opérades cellulaires et espaces de lacets itérés

Postnikov invariants of H-spaces

Product and other fine structure in polynomial resolutions of mapping spaces.

Product splittings for p-compact groups

Rational BV-algebra in string topology

Rational string topology

Some homotopy theoretical questions arising in Nielsen coincidence theory

Spaces of polynomials with roots of bounded multiplicity

Splittings of Spaces CX.

Strongly homotopy-commutative monoids revisited.

?SU (3) splits after four suspensions, but not two.

Sur l'homologie de l'espace des lacets d'une variété compacte

Suspension and loop objects and representability of tracks.

Currently displaying 61 – 80 of 106