On the cohomology ring of the free loop space of a wedge of spheres.
Mohammad Parhizgar (1997)
Mathematica Scandinavica
Waldhausen, Friedhelm (1996)
Documenta Mathematica
Vagn Lundsgaard Hansen (1974)
Compositio Mathematica
Manoharan, P. (2002)
International Journal of Mathematics and Mathematical Sciences
Stewart Priddy, Michael Barratt (1972)
Commentarii mathematici Helvetici
C.A. McGibbon, J.A. Neisendorfer (1984)
Commentarii mathematici Helvetici
Zheng-Xu He (1984)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Si definisce il gruppo di —omotopia di un singolo modulo e si introduce la nozione di equivalenza -omotopica debole. Sotto determinate condizioni per l'anello di base oppure per i moduli considerati, le equivalenze -omotopiche deboli coincidono con le equivalenze -omotopiche (forti).
Clemens Berger (1996)
Annales de l'institut Fourier
L’espace des configurations de points distincts de admet une filtration naturelle qui est induite par les inclusions des dans . 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 -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.
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 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.
Ahearn, Stephen T., Kuhn, Nicholas J. (2002)
Algebraic & Geometric Topology
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.
Yves Félix, Jean-Claude Thomas (2008)
Bulletin de la Société Mathématique de France
Let be a 1-connected closed manifold of dimension and be the space of free loops on . M.Chas and D.Sullivan defined a structure of BV-algebra on the singular homology of , . When the ring of coefficients is a field of characteristic zero, we prove that there exists a BV-algebra structure on the Hochschild cohomology which extends the canonical structure of Gerstenhaber algebra. We construct then an isomorphism of BV-algebras between and the shifted homology . We also prove that the...
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 . We prove that the loop homology of is isomorphic to the Hochschild cohomology of the cochain algebra with coefficients in . Some explicit computations of the loop product and the string bracket are given.
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.
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.
R.M. Vogt (1982)
Manuscripta mathematica
Brinkmeier, Michael (2000)
Documenta Mathematica
Mark Mahowald, William Richter (1991)
Mathematische Zeitschrift
Yves Félix, Daniel Tanré (1992)
Annales scientifiques de l'École Normale Supérieure
Baues, H.-J., Jibladze, M. (2001)
Georgian Mathematical Journal