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Subword complexes in Coxeter groups. (English) Zbl 1069.20026
One of the fundamental results in the theory of combinatorial-topological Coxeter groups is that Björner has shown that intervals in the weak Bruhat ordering are homotopy equivalent to balls or spheres. This work is analogous, or even sharper, where the authors demonstrate that the set of all subwords of an ordered list is homeomorphic to balls or spheres. The main result here depends on shellability of subword complexes. The authors raise some serious open questions at the end, and they might be answered soon. In brief, the article is a creative addition to the subject.

MSC:
20F55 Reflection and Coxeter groups (group-theoretic aspects)
06A11 Algebraic aspects of posets
05E15 Combinatorial aspects of groups and algebras (MSC2010)
05E25 Group actions on posets, etc. (MSC2000)
13F55 Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes
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