On Kan fibrations for Maltsev algebras.
On Kann's conditiion
On minimal models in integral homotopy theory.
On Stanley-Reisner rings
On the construction of the Kan loop group.
On the homology of mapping spaces
Following a Bendersky-Gitler idea, we construct an isomorphism between Anderson’s and Arone’s complexes modelling the chain complex of a mapping space. This allows us to apply Shipley’s convergence theorem to Arone’s model. As a corollary, we reduce the problem of homotopy equivalence for certain “toy” spaces to a problem in homological algebra.
On the Number of Faces of Simplicial Complexes and the Purity of Frobenius.
Optimal decision trees on simplicial complexes.
Ordinary and directed combinatorial homotopy, applied to image analysis and concurrency.
Reedy categories which encode the notion of category actions
We study a certain type of action of categories on categories and on operads. Using the structure of the categories Δ and Ω governing category and operad structures, respectively, we define categories which instead encode the structure of a category acting on a category, or a category acting on an operad. We prove that the former has the structure of an elegant Reedy category, whereas the latter has the structure of a generalized Reedy category. In particular, this approach gives a new way to regard...
Remarks about the Eilenberg-Zilber type decomposition in cosimplicial sets
Representation stability for syzygies of line bundles on Segre–Veronese varieties
The rational homology groups of packing complexes are important in algebraic geometry since they control the syzygies of line bundles on projective embeddings of products of projective spaces (Segre–Veronese varieties). These complexes are a common generalization of the multidimensional chessboard complexes and of the matching complexes of complete uniform hypergraphs, whose study has been a topic of interest in combinatorial topology. We prove that the multivariate version of representation stability,...
Representation-finite algebras and multiplicative bases.
Separable morphisms of simplicial sets.
Shellability and the strong gcd-condition.
Simplicial and categorical diagrams, and their equivariant applications.
Simplicial approximation.
Simplicial crossed modules and mapping cones.
Simplicial groups as models for -types
Simplicial matrices and the nerves of weak -categories I: Nerves of bicategories.