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Inverse limit slender groups

Volume 261 / 2023

Gregory R. Conner, Wolfgang Herfort, Curtis Kent, Petar Pavešić Fundamenta Mathematicae 261 (2023), 273-295 MSC: Primary 54B25; Secondary 54B35, 54H20, 54C. DOI: 10.4064/fm118-12-2022 Published online: 20 March 2023

Abstract

Classically, an abelian group $G$ is said to be slender if every homomorphism from the countable product $\mathbb Z^{\mathbb N}\mathbb N$ to $G$ factors through the projection to some finite product $\mathbb Z^n$. Various authors have proposed generalizations to non-commutative groups; this has resulted in a plethora of similar but not completely equivalent concepts. In the first part of this work we present a unified treatment of these concepts and examine how they are related. In the second part of the paper we study slender groups in the context of co-small objects in certain categories, and give several new applications, including the proof that certain homology groups of Barratt–Milnor spaces are cotorsion groups, and a universal coefficient theorem for Čech cohomology with coefficients in a slender group.

Authors

  • Gregory R. ConnerDepartment of Mathematics
    Brigham Young University
    Provo, UT 84602, USA
    e-mail
  • Wolfgang HerfortInstitute for Analysis and Scientific Computation
    Technische Universität Wien
    1040 Wien, Austria
    e-mail
  • Curtis KentDepartment of Mathematics
    Brigham Young University
    Provo, UT 84602, USA
    e-mail
  • Petar PavešićFaculty of Mathematics and Physics
    University of Ljubljana
    1000 Ljubljana, Slovenia
    and
    Institute of Mathematics, Physics, and Mechanics
    1000 Ljubljana, Slovenia
    e-mail

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