Cell-like mappings. I

Lacher, R. C.

doi:10.2140/pjm.1969.30.717

Cited by 86 publications

(42 citation statements)

References 26 publications

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“…The wider concept of a cell-like space was introduced by Lacher [11]. Cell-like maps have been studied by Lacher [12]. For a nice survey on the subject including a comprehensive bibliography, see [15].…”

Section: Proof Consider the Commutative Diagrammentioning

confidence: 99%

Some remarks on configuration spaces

Raptis¹

2011

Proc. Amer. Math. Soc.

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Abstract. This paper studies the homotopy type of the configuration spaces F n (X) by introducing the idea of configuration spaces of maps. For every map f : X → Y , the configuration space F n (f ) is the space of configurations in X that have distinct images in Y . We show that the natural maps F n (X) ← F n (f ) → F n (Y ) are homotopy equivalences when f is a proper cell-like map between d-manifolds. We also show that the best approximation to X → F n (X) by a homotopy invariant functor is given by the n-fold product map.

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Section: Proof Consider the Commutative Diagrammentioning

confidence: 99%

Some remarks on configuration spaces

Raptis¹

2011

Proc. Amer. Math. Soc.

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“…(iv) Any cell-like map [20] between Q-manifolds is arbitrarily close to a homeomorphism. This also shows that M Q Š Q.…”

Section: Appendix a Fibering Q-manifoldsmentioning

confidence: 99%

Obstructions to stably fibering manifolds

Steimle

2012

Geom. Topol.

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Is a given map between compact topological manifolds homotopic to the projection map of a fiber bundle? In this paper obstructions to this question are introduced with values in higher algebraic K -theory. Their vanishing implies that the given map fibers stably. The methods also provide results for the corresponding uniqueness question; moreover they apply to the fibering of Hilbert cube manifolds, generalizing results by Chapman and Ferry.19J10, 55R10; 57N20

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“…In other words, Á is a surjection for which the preimage of any point is contractible. Since, by the induction hypothesis, each E (v x ) is also polyhedral, Á is a cell-like map (for a de…nition see Lacher (1969), p. 718). For cell-like maps on polyhedra Corollary 1.3 of Lacher ((1969), p. 720) implies that the map is a homotopy equivalence.…”

Section: Figure 3: the Set Of Nash Equilibria Is Homotopy-equivalent mentioning

confidence: 99%

“…Since, there, a pure strategy induces choices only at decision points that can be reached under this strategy, the embedding from Lemma 2 has to be rede…ned. Moreover, for the reduced normal form, the convention, how to extend (11) to decision points that cannot be reached, does not apply, because S i (y) = R i (x) \ S i (y) for all y 2 P ¡1 (x) and all x 2 X i .…”

Section: Examplementioning

confidence: 99%

The simple geometry of perfect information games

Demichelis

Ritzberger

Swinkels

2004

International Journal of Game Theory

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Perfect information games have a particularly simple structure of equilibria in the associated normal form. For generic such games each of the finitely many connected components of Nash equilibria is contractible. For every perfect information game there is a unique connected and contractible component of subgame perfect equilibria. Finally, the graph of the subgame perfect equilibrium correspondence, after a very mild deformation, looks like the space of perfect information extensive form games.

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Cell-like mappings. I

Cited by 86 publications

References 26 publications

Some remarks on configuration spaces

Some remarks on configuration spaces

Obstructions to stably fibering manifolds

The simple geometry of perfect information games

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