Related papers: On the homotopy theory of arrangements, II
We survey two decades of work on the (sequential) topological complexity of configuration spaces of graphs (ordered and unordered), aiming to give an account that is unifying, elementary, and self-contained. We discuss the traditional…
In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed…
We endow categories of non-symmetric operads with natural model structures. We work with no restriction on our operads and only assume the usual hypotheses for model categories with a symmetric monoidal structure. We also study categories…
These course note first provide an introduction to secondary characteristic classes and differential cohomology. They continue with a presentation of a stable homotopy theoretic approach to the theory of differential extensions of…
This paper surveys work on generalized Johnson homomorphisms and tools for studying them. The goal is to unite several related threads in the literature and to clarify existing results and relationships among them using Hodge theory. We…
We show that if the fundamental groups of the complements of two line arrangements in the complex projective plane are isomorphic to the same direct sum of free groups, then the complements of the arrangements are homotopy equivalent. For…
In the first part of this paper, we consider, in the context of an arbitrary hyperplane arrangement, the map between compactly supported cohomology to the usual cohomology of a local system. A formula (i.e., an explicit algebraic de Rham…
This note was originated many years ago as my reaction to questions of several people how free strongly homotopy algebras can be described and what can be said about the structure of the universal enveloping A(m)-algebra of an L(m)-algebra,…
We use the wrinkling theorem proven in Y. Eliashberg and N. Mishachev, "Wrinkling of smooth mappings and its applications - I", Invent. Math., 130(1997), 345-369, to fully describe the homotopy type of the space of S-immersions, i.e.…
A systematic study of the contributions at infinity for the cohomology of variations of polarized Hodge structures over quasicompact K\"ahler manifolds. Several isomorphisms between different cohomologies given.
This paper has inappropriate amounts of overlap with the following papers also written by the authors or their collaborators: gr-qc/0506135, gr-qc/0207026, gr-qc/0502059, gr-qc/0502061, gr-qc/0510037, and others.
We describe the duality between different geometries which arises by considering the classical and quantum harmonic map problem. To appear in ``Essays on Mirror Manifolds II''.
It is well known since Stasheff's work that 1-fold loop spaces can be described in terms of the existence of higher homotopies for associativity (coherence conditions) or equivalently as algebras of contractible non-symmetric operads. The…
A review article on perturbation theory
Given a small category C, we show that there is a universal way of expanding C into a model category, essentially by formally adjoining homotopy colimits. The technique of localization becomes a method for imposing `relations' into these…
Let $D$ be a large category which is cocomplete. We construct a model structure (in the sense of Quillen) on the category of small functors from $D$ to simplicial sets. As an application we construct homotopy localization functors on the…
This is a survey of Rational Homotopy Theory, intended for a Mathematical Physics readership.
A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…
Adopting the global approach to tangent bundles of order two established in[1], we develop this approach to find new results. We also generalize various results of [3], [4] and [6] to the geometry of tangent bundles of order two.
We will review the main results concerning the automorphism groups of saturated structures which were obtained during the two last decades. The main themes are: the small index property in the countable and uncountable cases; the…