The theory of compact vector fields and some of its applications to topology of functional spaces (I)

A. Granas

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A. Granas (1960)

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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...

There are no Phantom Pairs of Mappings to 1-Dimensional CW-Complexes

Sibe Mardešić (2007)

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Two mappings from a CW-complex to a 1-dimensional CW-complex are homotopic if and only if their restrictions to finite subcomplexes are homotopic.

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I. Altun, D. Turkoglu (2007)

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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)

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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.

Gradient homotopies of gradient vector fields

A. Parusiński (1990)

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Set theoretical approach to the disconnection theory of the Euclidean space

Karol Borsuk (1950)

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On the homotopy type of $Diff (M^{n})$ and connected problems

Dan Burghelea (1973)

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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 $C^{\infty}$ -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 $Diff (D^{n}, \partial D^{n}), {Top}_{n}$ , ${Top}_{n} / O_{n}$ 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)

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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 $u \in T_{x} M$ , $u^{H}$ 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 $Λ (u) = γ_{1} (h (u)) Λ (g, K) + γ_{2} (h (u)) u^{H} \land u^{V},$ where $γ_{1}$ , $γ_{2}$ are smooth real functions...

On the Stark-Shintani units and the ideal class groups in the cyclotomic $ℤ_{p}$ -extensions of class fields over real quadratic fields

Tsuyoshi Itoh (2002)

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Topological degree for ultimately compact multivalued vector fields in topological vector spaces

Lj. Gajić (1987)

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