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Category with a natural cone

Francisco Díaz, Sergio Rodríguez-Machín (2006)

Open Mathematics

Generally, in homotopy theory a cylinder object (or, its dual, a path object) is used to define homotopy between morphisms, and a cone object is used to build exact sequences of homotopy groups. Here, an axiomatic theory based on a cone functor is given. Suspension objects are associated to based objects and cofibrations, obtaining homotopy groups referred to an object and relative to a cofibration, respectively. Exact sequences of these groups are built. Algebraic and particular examples are given....

c-continuous fundamental groups

Karl Gentry, Hughes Hoyle (1972)

Fundamenta Mathematicae

Čech cohomology and covering dimension for topological spaces

Kiiti Morita (1975)

Fundamenta Mathematicae

Cobordisme d'immersions

Pierre Vogel (1974)

Annales scientifiques de l'École Normale Supérieure

Co-H-grupos: Obstrucción a la commutatividad y aplicaciones centrales.

J. L. Navarro (1981)

Collectanea Mathematica

Computing the abelian heap of unpointed stable homotopy classes of maps

Lukáš Vokřínek (2013)

Archivum Mathematicum

An algorithmic computation of the set of unpointed stable homotopy classes of equivariant fibrewise maps was described in a recent paper [4] of the author and his collaborators. In the present paper, we describe a simplification of this computation that uses an abelian heap structure on this set that was observed in another paper [5] of the author. A heap is essentially a group without a choice of its neutral element; in addition, we allow it to be empty.

Comultiplications of the Wedge of Two Moore Spaces

Marek Golasiński, Daciberg Gonçalves (1998)

Colloquium Mathematicae

Connectedness of Certain Subsets of Locally Convex Spaces.

George Luna (1975)

Mathematische Annalen

Constructing manifolds by homotopy equivalences I. An obstruction to constructing PL-manifolds from homology manifolds

Hajime Sato (1972)

Annales de l'institut Fourier

We aim at constructing a PL-manifold which is cellularly equivalent to a given homology manifold $M^{n}$ . The main theorem says that there is a unique obstruction element in $H_{n - 4} (M, ℋ^{3})$ , where $ℋ^{3}$ is the group of 3-dimensional PL-homology spheres modulo those which are the boundary of an acyclic PL-manifold. If the obstruction is zero and $M$ is compact, we obtain a PL-manifold which is simple homotopy equivalent to $M$ .