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We present a characterization of cotorsion-free abelian groups in terms of homomorphisms from fundamental groups of Peano continua, which aligns naturally with the generalization of slenderness to non-abelian groups. In the process, we calculate the first homology group of the Griffiths twin cone.
Known and new results on free Boolean topological groups are collected. An account of properties which these groups share with free or free Abelian topological groups and properties specific of free Boolean groups is given. Special emphasis is placed
We prove the formula $TC(Gast H)=max{TC(G), TC(H), cd(Gtimes H)}$ for the topological complexity of the free product of discrete groups with cohomological dimension >2.
The present note surveys my research related to generalizing notions of abelian group theory to non-commutative case and applying them particularly to investigate fundamental groups.
Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space, namely atoms
We study the homology of free loop spaces via techniques arising from the theory of topological coHochschild homology (coTHH). Topological coHochschild homology is a topological analogue of the classical theory of coHochschild homology for coalgebras