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math.AT2025
Posets of decompositions in spherical buildings
Kevin Ivan Piterman, John Shareshian, Volkmar Welker
We propose definitions of the common bases complex, the poset of decompositions, and the poset of partial decompositions for arbitrary spherical buildings. We show that the poset o…
math.AT2025
On the homology of simplicial and cubical sets with symmetries
Curtis Greene, Volkmar Welker, Georg Wille
We study the homology of simplicial and cubical sets with symmetries. These are simplicial and cubical sets with additional maps expressing the symmetries of simplices and cubes. W…