On Combinatorial Descriptions of Homotopy Groups of ΣK(π, 1)∗
نویسنده
چکیده
We will give a combinatorial description of homotopy groups of ΣK(π, 1). In particular, all of the homotopy groups of the 3-sphere are combinatorially given.
منابع مشابه
1 4 A ug 1 99 5 ON COMBINATORIAL DESCRIPTIONS OF HOMOTOPY GROUPS OF Σ K ( π , 1 )
We give a combinatorial description of homotopy groups of ΣK(π, 1). In particular, all of the homotopy groups of the 3sphere are combinatorially given.
متن کاملHomotopy groups of suspended classifying spaces: An experimental approach
When the results of a computer program are confronted to some theorems proved on a theoretical basis three situations can occur: there can be an agreement between both approaches, the computer program can obtain calculations not covered by the theorems, or a discrepancy can be found between both methods. In this note we report on a work where the three above mentioned situations happen. We have...
متن کاملOn Combinatorial Descriptions of Homotopy Groups of Certain Spaces
We will give a combinatorial description of the homotopy groups for the suspension ofK(π, 1) and wedges of 2-spheres. In particular, all of the homotopy groups of the 2-sphere are given as the centers of certain combinatorially described groups.
متن کاملOn homotopy groups of the suspended classifying spaces
In this paper, we determine the homotopy groups π4(ΣK(A, 1)) and π5(ΣK(A, 1)) for abelian groups A by using the following methods from group theory and homotopy theory: derived functors, the Carlsson simplicial construction, the Baues-Goerss spectral sequence, homotopy decompositions and the methods of algebraic K-theory. As the applications, we also determine πi(ΣK(G, 1)) with i = 4, 5 for som...
متن کاملCombinatorial group theory and the homotopy groups of finite complexes
A description of homotopy groups of the 2-dimensional sphere in terms of combinatorial group theory was discovered by the second author in 1994 and given in his thesis [25], with a published version in [27]. In this article we give a combinatorial description of the homotopy groups of k-dimensional spheres with k ≥ 3. The description is given by identifying the homotopy groups as the center of ...
متن کامل