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I wanted to ask how to understand what a 2-polyhedron is and what the Collapsibility of Zeemans Conjecture $K \times I$ means in a geometric sense? How do I visualize the collapse? Or where can I find good books on this subject?

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Are you familiar with these notes?

Alexander Kupers, "Zeeman's Conjecture," 2017. PDF download.

Fig4

Kupers refers to this as "a good reference":

Sergei Matveev and Dale Rolfsen, "Zeeman’s collapsing conjecture," Two-dimensional homotopy and combinatorial group theory, London Math. Soc. Lecture Note Ser., vol. 197, Cambridge Univ. Press, Cambridge, 1993.

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  • $\begingroup$ Thank you very much. If I get it right a 2-polyhedron is in fact just a 2 dimensional simplicial complex and collapsing this 2-polyhedron $K$ with $K \times I$ means in fact that it is "expanded" to a 3 dimensional object and then collapses to a point? $\endgroup$
    – LogicTheorist
    Commented Dec 23, 2020 at 8:24
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    $\begingroup$ @LogicTheorist Lure gives a nice and short account here of the polyhedron category :math.ias.edu/~lurie/937notes/937Lecture2.pdf The main point being that a finite polyhedron is essentially the realization of a finite simplicial complex. It does not have a distinguished triangulation, but rather a class of them. $\endgroup$
    – Connor Malin
    Commented Dec 27, 2020 at 19:33

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