# The harmonic archipelago as a universal locally free group

```@article{Hojka2015TheHA,
title={The harmonic archipelago as a universal locally free group},
author={Wolfram Hojka},
journal={Journal of Algebra},
year={2015},
volume={437},
pages={44-51}
}```
• Wolfram Hojka
• Published 1 September 2015
• Mathematics
• Journal of Algebra
8 Citations

### Archipelago groups

• Mathematics
• 2014
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

### Cotorsion and wild homology

• Mathematics
• 2017
The classical concept of cotorsion of an abelian group is here characterized in the style of algebraic compactness, namely by the existence of solutions of certain systems of equations. This approach

### The fundamental group of reduced suspensions

• Mathematics
• 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

### Infinitary commutativity and fundamental groups of topological monoids.

• Mathematics
• 2020
The well-known Eckmann-Hilton Principle may be applied to prove that fundamental groups of \$H\$-spaces are commutative. In this paper, we identify an infinitary analogue of the Eckmann-Hilton

### The nonabelian product modulo sum

. It is shown that if { H n } n ∈ ω is a sequence of groups without invo- lutions, with 1 < | H n | ≤ 2 ℵ 0 , then the topologist’s product modulo the ﬁnite words is (up to isomorphism) independent

### On the Abelianization of Certain Topologist’s Products

• Mathematics
• 2017
For the topologist’s product \(\circledast _{i}G_{i}\) where each G i is the group of p elements, a description of its abelianization is provided. It turns out that the latter is isomorphic to

## References

SHOWING 1-10 OF 15 REFERENCES

### Archipelago groups

• Mathematics
• 2014
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

### The fundamental groups of subsets of closed surfaces inject into their first shape groups

• Mathematics
• 2005
We show that for every subset X of a closed surface M 2 and every x0 ∈ X, the natural homomorphism ϕ : π1(X, x0) → y π1(X, x0), from the fundamental group to the first shape homotopy group, is

### Rigidity of the Minimal Grope Group

• Mathematics
• 2006
. We give a systematic deﬁnition of the fundamental groups of gropes, which we call grope groups. We show that there exists a nontrivial homomorphism from the minimal grope group M to another grope

### Maps from the Minimal Grope to an Arbitrary Grope

• Mathematics
Int. J. Algebra Comput.
• 2013
It is proved that every continuous map from the minimal grope to another grope is nulhomotopic unless the other grope has a "branch" which is a copy of the minimalGrope.

### Remarks on certain pathological open subsets of 3-space and their fundamental groups

• Mathematics
• 1950
We shall consider several well known subsets of spherical 3-space S: the compact zero-dimensional set P described by Antoine [11 and the topological 3-cell C consisting of the "horned sphere" 2 of

### SINGULAR HOMOLOGY OF ONE-DIMENSIONAL SPACES

• Mathematics
• 1959
If X is a one-dimensional separable metric space, then wk(X) = 0 for all k > 1 (see [2]). Hence, such a space X is a K(r, 1), and w1(X) determines the singular homology of X. The principal result of

### The recognition problem: What is a topological manifold?

setting, difficult to come by. A good solution probably should not involve the notion of homogeneity (see Supplement 5) since, in applications, the spaces constructed which are to be checked are