64 citations · 361 across the 27 of their papers we have counts for
29 papers
Convex decomposition spaces and Crapo complementation formula
Imma Gálvez-Carrillo, Joachim Kock, Andrew Tonks
We establish a Crapo complementation formula for the Möbius function in a general decomposition space in terms of a convex subspace and its complement: $μ^X \simeq μ^…
The Hurewicz theorem for cubical homology
Daniel Carranza, Chris Kapulkin, Andrew Tonks
We give an elementary proof of the Hurewicz theorem relating homotopy and homology groups of a cubical Kan complex. Our approach is based on the notion of a loop space of a cubical…
Gabriel-Zisman Cohomology and spectral sequences
Imma Gálvez-Carrillo, Frank Neumann, Andrew Tonks
Extending constructions by Gabriel and Zisman, we develop a functorial framework for the cohomology and homology of simplicial sets with very general coefficient systems given by f…
Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation
Imma Gálvez-Carrillo, Ralph M. Kaufmann, Andrew Tonks
We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for m…
The diagonal of the associahedra
Naruki Masuda, Hugh Thomas, Andy Tonks +1
This paper introduces a new method to solve the problem of the approximation of the diagonal for face-coherent families of polytopes. We recover the classical cases of the simplice…
Decomposition spaces and restriction species
Imma Gálvez-Carrillo, Joachim Kock, Andrew Tonks
We show that Schmitt's restriction species (such as graphs, matroids, posets, etc.) naturally induce decomposition spaces (a.k.a. unital 2-Segal spaces), and that their associated…