A Generalization of the Vietoris-Begle Theorem

Dydak, Jerzy; Kozlowski, George

doi:10.2307/2046061

Cited by 6 publications

(6 citation statements)

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“…We show that each fibre of this map is a disc. As Z 1 is contractible, this shows (using, for instance, [3] or [5]), that Z is contractible.…”

Section: Fibres Of the Canonical Mapmentioning

confidence: 91%

A triangulation of a homotopy-Deligne-Mumford compactification of the Moduli of curves

Gadgil¹

2010

Preprint

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We construct a triangulation of a compactification of the Moduli space of a surface with at least one puncture that is closely related to the Deligne-Mumford compactification. Specifically, there is a surjective map from the compactification we construct to the Deligne-Mumford compactification so that the inverse image of each point is contractible. In particular our compactification is homotopy equivalent to the Deligne-Mumford compactification.

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“…We show that each fibre of this map is a disc. As Z 1 is contractible, this shows (using, for instance, [3] or [5]), that Z is contractible.…”

Section: Fibres Of the Canonical Mapmentioning

confidence: 91%

A triangulation of a homotopy-Deligne-Mumford compactification of the Moduli of curves

Gadgil¹

2010

Preprint

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“…To be precise, by a leveled tree in the sequel we will mean a rooted (not necessary planar) tree T together with a surjective map L from the set of its non-leaf nodes to some finite ordinal that respects the partial order ≺ induced by T . 7 We will say that a leveled tree (T, Similarly we can define the poset Φ level (n) of leveled fans. Graphically the levels of a fan can be represented by concentric circles around the root: Later on we will not distinguish between Φ level (n) and Ψ level ([n + 1]).…”

Section: Permutohedron and Leveled Treesmentioning

confidence: 99%

Section: Permutohedron and Leveled Treesmentioning

confidence: 99%

Associahedron, Cyclohedron and Permutohedron as compactifications of configuration spaces

Lambrechts¹,

Turchin²,

Volic³

2010

Bull. Belg. Math. Soc. Simon Stevin

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As in the case of the associahedron and cyclohedron, the permutohedron can also be defined as an appropriate compactification of a configuration space of points on an interval or on a circle. The construction of the compactification endows the permutohedron with a projection to the cyclohedron, and the cyclohedron with a projection to the associahedron. We show that the preimages of any point via these projections might not be homeomorphic to (a cell decomposition of) a disk, but are still contractible. We briefly explain an application of this result to the study of knot spaces from the point of view of the Goodwillie-Weiss manifold calculus.

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“…The case of cell-like maps and finite inductive dimension now follows from [21, Theorems 4.3.1 and 10.4.5] if D (and p −1 (D)) is compact, respectively, from [20] in the general case. The other case for cell-like maps is contained in [66] if D (and p −1 (D)) is compact, respectively, in [19] in the general case. See also [42,Theorem 2.19].…”

Section: Examples Of (Fm)-compact-homotopy-bijectionsmentioning

confidence: 99%

Merging of degree and index theory

Väth

2006

Fixed Point Theory Appl.

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The topological approaches to find solutions of a coincidence equation "Equation missing" can roughly be divided into degree and index theories. We describe how these methods can be combined. We are led to a concept of an extended degree theory for function triples which turns out to be natural in many respects. In particular, this approach is useful to find solutions of inclusion problems "Equation missing". As a side result, we obtain a necessary condition for a compact AR to be a topological group.

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A Generalization of the Vietoris-Begle Theorem

Abstract: ABSTRACT. A theorem is proved which generalizes both the Vietoris-Begle theorem and the cell-like theorem for spaces of finite defomation dimension. The proof is geometric and uses a double mapping cylinder trick.

Cited by 6 publications

References 0 publications

A triangulation of a homotopy-Deligne-Mumford compactification of the Moduli of curves

A triangulation of a homotopy-Deligne-Mumford compactification of the Moduli of curves

Associahedron, Cyclohedron and Permutohedron as compactifications of configuration spaces

Merging of degree and index theory

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