Abstract
For a given compact PL-manifold X, one studies the category CM(X) of combinatorial-manifold structures on X, where objects are abstract simplicial complexes with geometric realization PL-homeomorphic to X and the morphisms are "combinatorial subdivisions." The geometric realization BCM(X) of the nerve of CM(X) is announced to be homotopy equivalent to the classifying space BPL(X) of the simplicial group PL(X): \(B{\text{CM}}(X) \approx B{\text{PL}}(X)\). Bibliography: 8 titles.
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Anderson, L., Mnev, N. Triangulations of Manifolds and Combinatorial Bundle Theory: an Announcement. Journal of Mathematical Sciences 113, 755–758 (2003). https://doi.org/10.1023/A:1021223015807
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DOI: https://doi.org/10.1023/A:1021223015807