Related papers: On The Acyclic MacPhersonian

Around 1967, Arveson invented a striking noncommutative generalization of classical $H^\infty$, known as {\em subdiagonal algebras}, which include a wide array of examples of interest to operator theorists. Their theory extends that of the…

This is an expended and revised version of the preprint "Schematization of homotopy types". The purpose of this work is to introduce a notion of \emph{affine stacks}, which is a homotopy version of the notion of affine schemes, and to give…

We prove that random hypergraphs are asymptotically almost surely resiliently Hamiltonian. Specifically, for any $\gamma>0$ and $k\ge3$, we show that asymptotically almost surely, every subgraph of the binomial random $k$-uniform hypergraph…

Cyclic cohomology has been recently adapted to the treatment of Hopf symmetry in noncommutative geometry. The resulting theory of characteristic classes for Hopf algebras and their actions on algebras allows to expand the range of…

Homotopy type theory is a modern foundation for mathematics that introduces the univalence axiom and is particularly suitable for the study of homotopical mathematics and its formalization via proof assistants. In order to better comprehend…

The Anick spaces play a key role in an unstable filtration of the stable homotopy of V(0) to produce secondary EHP sequences. This work establishes that the Anick spaces are homotopy associative and homotopy commutative H-spaces, and that…

An error in the paper [J. Math. Phys. 43, 6343 (2002); math-ph/0207009] is corrected. Further explanation is given.

Let $\vec C_m$ and $\vec C_n$ be directed cycles of length $m$ and $n$, with $m,n \ge 3$, and let $P(\vec C_m \mathbin{\Box} \vec C_n)$ be the digraph that is obtained from the Cartesian product $\vec C_m \mathbin{\Box} \vec C_n$ by…

The Grassmannian, which is the manifold of all $k$-dimensional subspaces in the Euclidean space $\mathbb{R}^n$, was decomposed through three equivalent methods connecting combinatorial geometries, Schubert cells and convex polyhedra by…

In 2002, Biss investigated on a kind of fibration which is called rigid covering fibration (we rename it by rigid fibration) with properties similar to covering spaces. In this paper, we obtain a relation between arbitrary topological…

This paper contains an overview of background from stable homotopy theory used by Freed--Hopkins in their work on invertible extended topological field theories. We provide a working guide to the stable homotopy category, to the Steenrod…

We consider normal affine T-varieties X endowed with an action of finite abelian group G commuting with the action of T. For such varieties we establish the existence of G-equivariant geometrico-combinatorial presentations in the sense of…

This is an expository lecture, for the Abel bicentennial (Oslo, 2002), describing some recent work on the (small) quantum cohomology ring of Grassmannians and other homogeneous varieties.

In this paper, we describe a new approach to the problem of classification of transitive Anosov flows on 3-manifolds up to orbital equivalence. More specifically, generalizing the notion of Markov partition, we introduce the notion of…

We investigate forms of the Hopf invariant one problem in motivic homotopy theory over arbitrary base fields of characteristic not equal to $2$. Maps of Hopf invariant one classically arise from unital products on spheres, and one…

Kitchloo and Morava give a strikingly simple picture of elliptic cohomology at the Tate curve by studying a completed version of $S^1$-equivariant $K$-theory for spaces. Several authors (cf [ABG],[KM],[L]) have suggested that an equivariant…

In this paper we prove a tertiary index theorem which relates a spectral geometric and a homotopy theoretic invariant of an almost complex manifold with framed boundary. It is derived from the index theoretic and homotopy theoretic versions…

Let $D$ be a digraph of order $p\geq5$ with minimum degree at least $p-1$ and with minimum semi-degree at least $p/2-1$. In his excellent and renowned paper, ``Long Cycles in Digraphs" (Proc. London Mathematical Society (3), 42 (1981),…

This is one of a series papers which aim towards to solve the problem of determining automorphism groups of Frobenius groups. This one solves the problem in the case where the Frobenius kernels are elementary abelian and Frobenius…

By affine arithmetic is meant the set of affine consequences of Peano arithmetic. This is a continuous theory which is studied in the framework of affine logic, a sublogic of continuous logic. Affine arithmetic is undecidable. Also, its…