Results 161 to 170 of about 59,724 (184)
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Homotopy Groups of Transformation Groups
Canadian Journal of Mathematics, 1969In a previous paper (2) I defined the fundamental group σ(X, x0, G) of a group Gof homeomorphisms of a space X, and showed that if the transformation group admits a family of preferred paths, then σ(X, x0, G) can be represented as a group extension of π1(X, x0) by G. In this paper the homotopy groups of a transformation group are defined.
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2003
This beautiful and very interesting paper is firstly an exposition of the method of \textit{J. H. Conway} and \textit{J. C. Lagarias} [J. Comb. Theory, Ser. A 53, 183--208 (1990; Zbl 0741.05019)] to show the impossibility of certain tiling problems using groups of boundary words.
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This beautiful and very interesting paper is firstly an exposition of the method of \textit{J. H. Conway} and \textit{J. C. Lagarias} [J. Comb. Theory, Ser. A 53, 183--208 (1990; Zbl 0741.05019)] to show the impossibility of certain tiling problems using groups of boundary words.
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2022
As Goresky and MacPherson intersection homology is not the homology of a space, there is no preferred candidate for intersection homotopy groups. Here, they are defined as the homotopy groups of a simplicial set which P. Gajer associates to a couple $(X,\overline{p})$ of a filtered space and a perversity.
Chataur, David +2 more
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As Goresky and MacPherson intersection homology is not the homology of a space, there is no preferred candidate for intersection homotopy groups. Here, they are defined as the homotopy groups of a simplicial set which P. Gajer associates to a couple $(X,\overline{p})$ of a filtered space and a perversity.
Chataur, David +2 more
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2016
This chapter continues to study homotopy theory displaying construction of a sequence of covariant functors \(\pi _n\) given by W. Hurewicz (1904–1956) in 1935 from topology to algebra by extending the concept of fundamental group, which is the first influential functor of homotopy theory invented by H. Poincare (1854–1912) in 1895.
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This chapter continues to study homotopy theory displaying construction of a sequence of covariant functors \(\pi _n\) given by W. Hurewicz (1904–1956) in 1935 from topology to algebra by extending the concept of fundamental group, which is the first influential functor of homotopy theory invented by H. Poincare (1854–1912) in 1895.
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On Products in Homotopy Groups
The Annals of Mathematics, 1946One of the outstanding problems in homotopy theory is that of determining the homotopy groups of simple spaces. Even for as simple a space as the n-sphere very little is known. In fact, in most cases, it is not known whether or not the homotopy groups are zero. J. H. C.
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Homotopy and the Fundamental Group
2006The results of the preceding chapter left a serious gap in our attempt to classify compact 2-manifolds up to homeomorphism: although we have exhibited a list of surfaces and shown that every compact connected surface is homeomorphic to one on the list, we still have no way of knowing when two surfaces are not homeomorphic.
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HOMOTOPY RINGOIDS AND HOMOTOPY GROUPS
The Quarterly Journal of Mathematics, 1954openaire +1 more source