A fixed-point theorem for face maps, or deletion-tolerant random finite sets

2025/05/27 by Hutchcroft, Tom, Monod, Nicolas, Tamuz, Omer
#Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2505.21484

Abstract

We establish a fixed-point theorem for the face maps that consist in deleting the ith entry of an ordered set. Furthermore, we show that there exists random finite sets of integers that are almost invariant under such deletions. Consequences for various monoids of order-preserving transformations of N are discussed in an appendix.

Citations

• The bounded cohomology of transformation groups of Euclidean spaces and discs

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