Geodesic
Combinatorial PL fiber bundles and fragmentation of a fiberwise homeomorphism
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XV, Tome 344 (2007), pp. 56-173 Cet article a éte moissonné depuis la source Math-Net.Ru

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Among other things, we prove that for any compact PL-manifold $X$ there is a homotopy equivalence $BPL(X)\approx BT(X)$, where $T(X)$ is the category of abstract aggregations of triangulations of $X$. As a result, we get a functorial pure combinatorial models for PL fiber bundles. Special attention is paid to the case $X=\mathbb R^n$ and the combinatorial model of the Gauss map of a combinatorial manifold. The key trick which makes the proof possible is a collection of lemmas describing the fragmentation of a fiberwise homeomorphism. 
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N. E. Mnev. Combinatorial PL fiber bundles and fragmentation of a fiberwise homeomorphism. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XV, Tome 344 (2007), pp. 56-173. http://geodesic.mathdoc.fr/item/ZNSL_2007_344_a2/

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