Related papers: Combinatorics of double loop suspensions, evaluati…

We give a particular choice of the higher Eilenberg-MacLane maps by a recursive formula.This choice leads to a simple description of the homotopy operations for simplicial Z/2-algebras.

We explore a relationship between topological properties of orbits of 2-cycles in the symplectomorphism group Symp(M) and the existence of rational curves in M. Under the absence of rational curves hypothesis, we show that evaluation map…

A poset-stratified space is a pair $(S, S \xrightarrow \pi P)$ of a topological space $S$ and a continuous map $\pi: S \to P$ with a poset $P$ considered as a topological space with its associated Alexandroff topology. In this paper we show…

Billey-Postnikov (BP) decompositions govern when Schubert varieties $X(w)$ decompose as bundles of smaller Schubert varieties. We further develop the theory of BP decompositions and show that, in finite type, they can be recognized by…

We study the Hopf algebra of double posets and two of its Hopf subalgebras, the Hopf algebras of plane posets and of posets "without N". We prove that they are free, cofree, self-dual, and we give an explicit Hopf pairing on these Hopf…

Constructive methods for matrices of multihomogeneous (or multigraded) resultants for unmixed systems have been studied by Weyman, Zelevinsky, Sturmfels, Dickenstein and Emiris. We generalize these constructions to mixed systems, whose…

Greenlees and Sadofsky showed that the classifying spaces of finite groups are self-dual with respect to Morava K-theory K(n). Their duality map was constructed using a transfer map. We generalize their duality map and prove a K(n)-version…

In a previous article, we introduced notions of finiteness obstruction, Euler characteristic, and L^2-Euler characteristic for wide classes of categories. In this sequel, we prove the compatibility of those notions with homotopy colimits of…

We define a birational map between labelings of a rectangular poset and its associated trapezoidal poset. This map tropicalizes to a bijection between the plane partitions of these posets of fixed height, giving a new bijective proof of a…

We use the combinatorial harmonic map theory to study the isometric actions of discrete groups on Hadamard spaces. Given a finitely generated group acting by automorphisms, properly discontinuously and cofinitely on a simplicial complex and…

We develop a new method to compute the homology groups of finite topological spaces (or equivalently of finite partially ordered sets) by means of spectral sequences giving a complete and simple description of the corresponding…

We study Cohen-Macaulay Hopf monoids in the category of species. The goal is to apply techniques from topological combinatorics to the study of polynomial invariants arising from combinatorial Hopf algebras. Given a polynomial invariant…

We consider the Newton stratification on Iwahori double cosets in the loop group of a reductive group. We describe a group-theoretic condition on the generic Newton point, called cordiality, under which the Newton poset (i.e. the index set…

Given a simply connected space $X$, there are several, a priori different, algebraic groups whose groups of $\mathbb Q$-points are isomorphic to the group of homotopy classes of homotopy automorphisms of the rationalization of $X$. We will…

We introduce a natural Hopf algebra structure on the space of noncommutative symmetric functions which was recently studied as a vector space by Rosas and Sagan. The bases for this algebra are indexed by set partitions. We show that there…

We extend some classical results - such as Quillen's Theorem A, the Grothendieck construction, Thomason's Theorem and the characterisation of homotopically cofinal functors - from the homotopy theory of small categories to polynomial monads…

Let $A$ be a regular ring over a field $k$, with $1/2\in k$ and dimension $d$. We discuss the Homotopy Conjecture of Madhav V. Nori, in the complete intersection case (meaning when the projective module in question if free, of rank at least…

Let M be a monoidal category endowed with a distinguished class of weak equivalences and with appropriately compatible classifying bundles for monoids and comonoids. We define and study homotopy-invariant notions of normality for maps of…

We investigate the dynamics of semigroups of rational maps on the Riemann sphere. To establish a fractal theory of the Julia sets of infinitely generated semigroups of rational maps, we introduce a new class of semigroups which we call…

Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…