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On the connection between the topological genus of certain polyhedra and the algebraic genus of their Hilton-Hopt quadratic forms.

Imre Bokor (1990)

Publicacions Matemàtiques

The Hilton-Hopf quadratic form is defined for spaces of the homotopy type of a CW complex with one cell each in dimensions 0 and 4n, K cells in dimension 2n and no other cells. If two such spaces are of the same topological genus, then their Hilton-Hopf quadratic forms are of the same weak algebraic genus. For large classes of spaces, such as simply connected differentiable 4-manifolds, the converse is also true, as long as the suspensions of the spaces are also of the same topological genus. This...

On the connectivity of finite subset spaces

Jacob Mostovoy, Rustam Sadykov (2012)

Fundamenta Mathematicae

We prove that the space $e x p_{k} ⋁ S^{m + 1}$ of nonempty subsets of cardinality at most k in a bouquet of m+1-dimensional spheres is (m+k-2)-connected. This, as shown by Tuffley, implies that the space $e x p_{k} X$ is (m+k-2)-connected for any m-connected cell complex X.

On the construction of the Kan loop group.

Waldhausen, Friedhelm (1996)

Documenta Mathematica

On the Detection of Some Elements in the Image of the Double Transfer Using K(2)-Theory.

Andrew Baker (1988)

Mathematische Zeitschrift

On the finiteness of the fundamental group of a compact shrinking Ricci soliton

Zhenlei Zhang (2007)

Colloquium Mathematicae

Myers's classical theorem says that a compact Riemannian manifold with positive Ricci curvature has finite fundamental group. Using Ambrose's compactness criterion or J. Lott's results, M. Fernández-López and E. García-Río showed that the finiteness of the fundamental group remains valid for a compact shrinking Ricci soliton. We give a self-contained proof of this fact by estimating the lengths of shortest geodesic loops in each homotopy class.

On the first homology of Peano continua

Gregory R. Conner, Samuel M. Corson (2016)

Fundamenta Mathematicae

We show that the first homology group of a locally connected compact metric space is either uncountable or finitely generated. This is related to Shelah's well-known result (1988) which shows that the fundamental group of such a space satisfies a similar condition. We give an example of such a space whose fundamental group is uncountable but whose first homology is trivial, showing that our result does not follow from Shelah's. We clarify a claim made by Pawlikowski (1998) and offer a proof of the...

On the fundamental group of a mapping space. An example

Vagn Lundsgaard Hansen (1974)

Compositio Mathematica

On the fundamental group of a space of sections.

E. Thomas, L.L. Larmore (1980)

Mathematica Scandinavica

On the Groups JOGX. I.

James E. McClure (1983)

Mathematische Zeitschrift

On the Growth of Homotopy Groups.

Hans Werner Henn (1986)

Manuscripta mathematica

On the homotopical classification of DJ-mappings of infnitely dimensional spheres

Bogdan Przeradzki (1984)

Fundamenta Mathematicae

On the homotopy category of Moore spaces and the cohomology of the category of abelian groups

Hans-Joachim Baues, Manfred Hartl (1996)

Fundamenta Mathematicae

The homotopy category of Moore spaces in degree 2 represents a nontrivial cohomology class in the cohomology of the category of abelian groups. We describe various properties of this class. We use James-Hopf invariants to obtain explicitly the image category under the functor chain complex of the loop space.

On the homotopy groups of a finite dimensional space.

C.A. McGibbon, J.A. Neisendorfer (1984)

Commentarii mathematici Helvetici

On the Homotopy of Non-Nilpotent Spaces.

Jean-Claude Hausmann (1981)

Mathematische Zeitschrift

On the Homotopy Properties of Thom Complexes.

René P. Held, Denis K. Sjerve (1973/1974)

Mathematische Zeitschrift

On the homotopy type of a chain algebra.

Benkhalifa, Mahmoud (2004)

Homology, Homotopy and Applications

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

Dan Burghelea (1973)

Annales de l'institut Fourier

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.The results are contained in Section 1 and Section...

On the homotopy type of (n-1)-connected (3n+1)-dimensional free chain Lie algebra

Mahmoud Benkhalifa, Nabilah Abughzalah (2005)

Open Mathematics

Let R be a subring ring of Q. We reserve the symbol p for the least prime which is not a unit in R; if R ⊒Q, then p=∞. Denote by DGL nnp, n≥1, the category of (n-1)-connected np-dimensional differential graded free Lie algebras over R. In [1] D. Anick has shown that there is a reasonable concept of homotopy in the category DGL nnp. In this work we intend to answer the following two questions: Given an object (L(V), ϖ) in DGL n3n+2 and denote by S(L(V), ϖ) the class of objects homotopy equivalent...

On the Hurewicz image of the cokernel J spectrum

Norihiko Minami (1998)

Fundamenta Mathematicae

On the Iterated Complex Transfer.

D. Carlisle, A. Baker, B.G24 Gray (1988)

Mathematische Zeitschrift

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