Search 206,553,498 papers from all fields of science

Search

Sign InCreate Free Account

Corpus ID: 55124577

The fundamental group of reduced suspensions

@article{Corson2017TheFG,
title={The fundamental group of reduced suspensions},
author={Samuel M. Corson and Wolfram Hojka},
journal={arXiv: Group Theory},
year={2017}
}

We classify pointed spaces according to the first fundamental group of their reduced suspension. A pointed space is either of so-called totally path disconnected type or of horseshoe type. These two camps are defined topologically but a characterization is given in terms of fundamental groups. Among totally path disconnected spaces the fundamental group is shown to be a complete invariant for a notion of topological equivalence weaker than that of homeomorphism.

We strengthen previous results on the fundamental groups of the Hawaiian earring and wild Peano continua. Let X be a path-connected, locally path-connected, first countable space which is not locally… Expand

The classical archipelago is a non-contractible subset of R3 which is homeomorphic to a disk except at one non-manifold point. Its fundamental group, A , is the quotient of the topologist’s product… Expand

In this paper, we develop the low dimensional homotopy theory required for weighted combinatorial group theory. In [S97], the usual concepts of generators and relators of group presentations are… Expand

To address the question “What is the foundation of science?” I base my response on the two substantive constructs of the question: science and foundation.