2017/08/31 by Baralic, Djordje, Grbic, Jelena, Vavpetic, Ales +1
#05E45 #52B22 #57Q05 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #K-Theory and Homology (math.KT)
paper · doi:10.48550/arxiv.1708.09565
Let k be the field \mathbbFp or the ring ℤ. We study combinatorial and topological properties of the universal simplicial complexes X(kn) and K(kn) whose simplices are certain unimodular subsets of kn. As a main result we show that X(kn), K(kn) and the links of their simplicies are homotopy equivalent to a wedge of spheres specifying the exact number of spheres in the corresponding wedge decompositions. This is a generalisation of Davis and Januszkiewicz's result that K(ℤn) and K(\mathbbF2n) are (n-2)-connected simplicial complexes. We discuss applications of these universal simplicial complexes to toric topology and number theory.