Scindement d’une équivalence d’homotopie en dimension
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Self homotopy equivalences of virtually nilpotent spaces.
E. Dror, W.G. Dwyer, D.M. Kann (1981)
Commentarii mathematici Helvetici
Shapes of saturated subsets of compacta
B. J. Ball (1974)
Colloquium Mathematicae
Simply connected coset complexes for rank 1 groups of Lie type.
Yoav Segev (1994)
Mathematische Zeitschrift
Some non-trivial PL knots whose complements are homotopy circles
Greg Friedman (2007)
Fundamenta Mathematicae
We show that there exist non-trivial piecewise linear (PL) knots with isolated singularities , n ≥ 5, whose complements have the homotopy type of a circle. This is in contrast to the case of smooth, PL locally flat, and topological locally flat knots, for which it is known that if the complement has the homotopy type of a circle, then the knot is trivial.
Some quantitative properties of shapes
Karol Borsuk (1976)
Fundamenta Mathematicae
Some Topological Properties of Kähler Manifolds and Homogeneous Spaces.
Willi Meier (1983)
Mathematische Zeitschrift
Stratified model categories
Jan Spaliński (2003)
Fundamenta Mathematicae
The fourth axiom of a model category states that given a commutative square of maps, say i: A → B, g: B → Y, f: A → X, and p: X → Y such that gi = pf, if i is a cofibration, p a fibration and either i or p is a weak equivalence, then a lifting (i.e. a map h: B → X such that ph = g and hi = f) exists. We show that for many model categories the two conditions that either i or p above is a weak equivalence can be embedded in an infinite number of conditions which imply the existence of a lifting (roughly,...
Subdivision yields Alexander duality on independence complexes.
Csorba, Péter (2009)
The Electronic Journal of Combinatorics [electronic only]
Sur certaines équivalences d'homotopies
M. Aubry, Jean-Michel Lemaire (1991)
Annales de l'institut Fourier
On sait qu’il y a 144 classes d’homotopies d’applications de dans lui-même dont la restriction à est homotope à l’identité: ce sont des exemples d’applications qui induisent l’identité en homologie et en homotopie. Plus généralement, soit un complexe de Poincaré 1-connexe de dimension , qui n’a pas le type d’homotopie rationnelle de : si est formel, nous montrons que le groupe des classes d’homotopies d’applications de dans , dont la restriction au -squelette est homotope à l’identité,...
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