Related papers: Loop homological invariants associated to real pro…

The problem of approximating the infinite dimensional space of all continuous maps from an algebraic variety $X$ to an algebraic variety $Y$ by finite dimensional spaces of algebraic maps arises in several areas of geometry and mathematical…

We compute the mod-2 cohomology of the collection of all symmetric groups as a Hopf ring, where the second product is the transfer product of Strickland and Turner. We first give examples of related Hopf rings from invariant theory and…

We derive actions for projective N=2 superspace ("hyperspace") from those for harmonic hyperspace, including that for nonabelian Yang-Mills (a new result). The method uses Wick rotation of the sphere from complex conjugate coordinates to…

We compute the integral homology of the space of paths in $\mathbb{C}P^n$ with endpoints in $\mathbb{R}P^n$, $n \ge 1$ and its algebra structure with respect to the Pontryagin-Chas-Sullivan product with $\mathbb{Z}/2$-coefficients.

Here we shall consider the topology and dynamics associated to a wide class of matchbox manifolds, including a large selection of tiling spaces and all minimal matchbox manifolds of dimension one. For such spaces we introduce topological…

We prove the projective plane $\rp^2$ is an absolute extensor of a finite-dimensional metric space $X$ if and only if the cohomological dimension mod 2 of $X$ does not exceed 1. This solves one of the remaining difficult problems (posed by…

Harmonic maps that minimise the Dirichlet energy in their homotopy classes are known as lumps. Lump solutions on real projective space are explicitly given by rational maps subject to a certain symmetry requirement. This has consequences…

Let M be a smooth, simply-connected, closed oriented manifold, and LM the free loop space of M. Using a Poincare duality model for M, we show that the reduced equivariant homology of LM has the structure of a Lie bialgebra, and we construct…

Recent work of Beben and Theriault on decomposing based loop spaces of highly connected Poincar\'e Duality complexes has yielded new methods for analysing the homotopy theory of manifolds. In this paper we will expand upon these methods,…

Let $\Lambda$ be a left and right noetherian ring. First, for $m,n\in\mathbb{N}\cup\{\infty\}$, we give equivalent conditions for a given $\Lambda$-module to be $n$-torsionfree and have $m$-torsionfree transpose. Using them, we investigate…

A projection space is a collection of spaces interrelated by the combinatorics of projection onto tensor factors in a symmetric monoidal background category. Examples include classical configuration spaces, orbit configuration spaces, the…

We introduce loop spaces (in the sense of derived algebraic geometry) into the representation theory of reductive groups. In particular, we apply the theory developed in our previous paper arXiv:1002.3636 to flag varieties, and obtain new…

In his Inventiones paper, Ziller (Invent. Math: 1-22, 1977) computed the integral homology as a graded abelian group of the free loop space of compact, globally symmetric spaces of rank 1. Chas and Sullivan (String Topology, 1999)showed…

We discuss inequalities between the values of \emph{homotopical and cohomological Poincar\'e polynomials} of the self-products of rationally elliptic spaces. For rationally elliptic quasi-projective varieties, we prove inequalities between…

This paper is a first of a series of three papers which study eta invariants for laminations. In this first paper, we extend the results of Higson and Roe to deal with regular (unbounded) operators and more importantly to take into account…

Abstract. Let G be a complex reductive group and A be an Abelian variety of dimension d over $\mathbb{C}$. We determine the Poincar\'e polynomials and also the mixed Hodge polynomials of the moduli space $\mathcal{M}_{A}^{H}(G)$ of G-Higgs…

In this short note we observe that the higher topological complexity of an iterated connected sum of real projective spaces is maximal possible. Unlike the case of regular TC, the result is accessible through easy mod 2 zero-divisor…

We introduce the notion of a logarithmic stable map from a minimal log prestable curve to a log twisted semi-stable variety of form $xy=0$. We study the compactification of the moduli spaces of such maps and provide a perfect obstruction…

We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under…

A new method is given for computing generators of the homology groups with integer coefficients for any finite $T_0$-space. An important role in this method is played by irreducible cycles which are defined here and give rise to continuous…