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Start Over Topic classifying space Publication Year Range More than 50 years ago Language english
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1. Characteristic classes for PL micro bundles

Author

Akihiro Tsuchiya

Subjects
57C50, Classifying space, Pure mathematics, 010308 nuclear & particles physics, General Mathematics, 010102 general mathematics, Prime number, Topology, Hopf algebra, 01 natural sciences, Characteristic class, 0103 physical sciences, 0101 mathematics, Mathematics
Abstract

Let BSPL be the classifying space of the stable oriented PL micro bundles. The purpose of this paper is to determine H*(BSPL:Zp) as a Hopf algebra over Zp, where p is an odd prime number. In this chapter, p is always an odd prime number.

Published
1971

2. A group of automorphisms of the homotopy groups

Author

Hiroshi Uehara

Subjects
Normal subgroup, Combinatorics, Homotopy group, Classifying space, Fundamental group, Automorphisms of the symmetric and alternating groups, General Mathematics, Bott periodicity theorem, Whitehead theorem, Automorphism, Topology, 56.0X, Mathematics
Abstract

It is well known that the fundamental group π1(X) of an arcwise connected topological space X operates on the n-th homotopy group πn(X) of X as a group of automorphisms. In this paper I intend to construct geometrically a group 𝒰(X) of automorphisms of πn(X), for every integer n ≥ 1, which includes a normal subgroup isomorphic to π1(X) so that the factor group of 𝒰(X) by π1(X) is completely determined by some invariant Σ(X) of the space X. The complete analysis of the operation of the group on πn(X) is given in §3, §4, and §5

Published
1951