Displaying similar documents to “The theory of compact vector fields and some of its applications to topology of functional spaces (I)”

Embedding proper homotopy types

M. Cárdenas, T. Fernández, F. F. Lasheras, A. Quintero (2003)

Colloquium Mathematicae

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We show that the proper homotopy type of any properly c-connected locally finite n-dimensional CW-complex is represented by a closed polyhedron in ℝ 2 n - c (Theorem I). The case n - c ≥ 3 is a special case of a general proper homotopy embedding theorem (Theorem II). For n - c ≤ 2 we need some basic properties of “proper” algebraic topology which are summarized in Appendices A and B. The results of this paper are the proper analogues of classical results by Stallings [17] and Wall [20] for finite...

Fixed point and homotopy result for mappings satisfying an implicit relation

I. Altun, D. Turkoglu (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper, we prove some fixed point theorems for single valued mappings satisfying an implicit relation on space with two metrics. In addition we give a homotopy result using our theorems.

G-ANR's with homotopy trivial fixed point sets

Sergey A. Antonyan (2007)

Fundamenta Mathematicae

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Let G be a compact group and X a G-ANR. Then X is a G-AR iff the H-fixed point set X H is homotopy trivial for each closed subgroup H ⊂ G.

On the homotopy type of Diff ( M n ) and connected problems

Dan Burghelea (1973)

Annales de l'institut Fourier

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This paper reports on some results concerning: a) The homotopy type of the group of diffeomorphisms Diff ( M n ) of a differentiable compact manifold M n (with C ∞ -topology). b) the result of the homotopy comparison of this space with the group of all homeomorphisms Homeo M n (with C o -topology). As a biproduct, one gets new facts about the homotopy groups of Diff ( D n , ∂ D n ) , Top n , Top n / O n and about the number of connected components of the space of topological and combinatorial pseudoisotopies. ...

Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold

Josef Janyška (2001)

Archivum Mathematicum

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Let M be a differentiable manifold with a pseudo-Riemannian metric g and a linear symmetric connection K . We classify all natural (in the sense of [KMS]) 0-order vector fields and 2-vector fields on T M generated by g and K . We get that all natural vector fields are of the form E ( u ) = α ( h ( u ) ) u H + β ( h ( u ) ) u V , where u V is the vertical lift of u ∈ T x M , u H is the horizontal lift of u with respect to K , h ( u ) = 1 / 2 g ( u , u ) and α , β are smooth real functions defined on R . All natural 2-vector fields are of the form Λ ( u ) = γ 1 ( h ( u ) ) Λ ( g , K ) + γ 2 ( h ( u ) ) u H ∧ u V , where γ 1 , γ 2 are smooth real functions...