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Mat. Sb., 2007, Volume 198, Number 4, Pages 79–94 (Mi msb1558)  

This article is cited in 1 scientific paper (total in 1 paper)

Asphericity and approximation properties of crossed modules

R. V. Mikhailov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: This paper is devoted to the study of the Baer invariants and approximation properties of crossed modules and $cat^1$-groups. Conditions are considered under which the kernels of crossed modules coincide with the intersection of the lower central series. An algebraic criterion for asphericity is produced for two-dimensional complexes having aspherical plus-construction. As a consequence it is shown that a subcomplex of an aspherical two-dimensional complex is aspherical if and only if its fundamental $cat^1$-group is residually soluble. Thus, a new formulation in group-theoretic terms is given to the Whitehead asphericity conjecture.
Bibliography: 25 titles.

DOI: https://doi.org/10.4213/sm1558

Full text: PDF file (549 kB)
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English version:
Sbornik: Mathematics, 2007, 198:4, 521–535

Bibliographic databases:

UDC: 512.544+515.145
MSC: Primary 20E26, 57M20; Secondary 18B40, 18G30, 18G50, 18G55, 20F14, 20F19, 20F34, 2
Received: 18.04.2006 and 28.11.2006

Citation: R. V. Mikhailov, “Asphericity and approximation properties of crossed modules”, Mat. Sb., 198:4 (2007), 79–94; Sb. Math., 198:4 (2007), 521–535

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Mikhailov R., Passi I.B.S., Lower Central and Dimension Series of Groups, Lecture Notes in Mathematics, 1952, Springer, Berlin–Heidelberg, 2009, xxii+346 pp.  crossref  mathscinet  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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