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Whitehead’s Asphericity Question and Its Relation to Other Open Problems

  • A. J. BerrickEmail author
  • J. A. Hillman
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

This note explores J. H. C. Whitehead’s 1941 question as to whether a subcomplex of an aspherical 2-complex need also have vanishing higher homotopy groups. Methods from \(L^{2}\)-cohomology are brought to bear on the question and relate it to other open problems on low-dimensional complexes—some introduced here—as well as open problems on group theory, such as the Kervaire–Laudenbach Conjecture, and on group algebras, like the Bass trace conjecture.

Keywords

Acyclic cover Cockcroft condition Cohomological dimension \(L^{2}\)-Betti Subaspherical complex Whitehead Conjecture 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsYale-NUS College, National University of SingaporeSingaporeSingapore
  2. 2.School of MathematicsUniversity of SydneyCamperdownAustralia

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