TOPOLOGICAL CHIRAL HOMOLOGY AND HOMOLOGICAL STABILITY FOR COMPLETIONS OF En-ALGEBRAS
نویسنده
چکیده
An interesting phenomenon is that the configuration space of particles on an open manifold has homology independent of the number of particles in a range increasing with the number of particles. Such configuration spaces are one of the simplest examples of topological chiral homology, which is a homology theory for n-dimensional manifolds taking values in spaces and taking En-algebras as coefficients. In this note we explain how many previous results on homological stability, including that for configuration spaces, fit into the framework of topological chiral homology and are a consequence of a general result by the author and Jeremy Miller.
منابع مشابه
Free Factorization Algebras and Homology of Configuration Spaces in Algebraic Geometry
We provide a construction of free factorization algebras in algebraic geometry and link factorization homology of a scheme with coefficients in a free factorization algebra to the homology of its (unordered) configuration spaces. As an application, this construction allows for a purely algebro-geometric proof of homological stability of configuration spaces. CONTENTS
متن کاملHomology for higher-rank graphs and twisted C*-algebras
We introduce a homology theory for k-graphs and explore its fundamental properties. We establish connections with algebraic topology by showing that the homology of a k-graph coincides with the homology of its topological realisation as described by Kaliszewski et al. We exhibit combinatorial versions of a number of standard topological constructions, and show that they are compatible, from a h...
متن کاملCyclic Cohomology of Certain Nuclear Fréchet and Df Algebras
We give explicit formulae for the continuous Hochschild and cyclic homology and cohomology of certain ⊗̂-algebras. We use well-developed homological techniques together with some niceties of the theory of locally convex spaces to generalize the results known in the case of Banach algebras and their inverse limits to wider classes of topological algebras. To this end we show that, for a continuou...
متن کاملStrongly Torsion Generated Groups from K-theory of Real C∗-algebras
We pursue the program initiated in [7], which consists of an attempt by means of K-theory to construct a strongly torsion generated group with prescribed center and integral homology in dimensions two and higher. Using algebraic and topological K-theory for real C∗-algebras, we realize such a construction up to homological dimension five. We also explore the limits of the K-theoretic approach.
متن کاملHomological Realization of Prescribed Abelian Groups via K-theory
Using algebraic and topological K-theory together with complex C∗-algebras, we prove that every abelian group may be realized as the centre of a strongly torsion generated group whose integral homology is zero in dimension one and isomorphic to two arbitrarily prescribed abelian groups in dimensions two and three.
متن کامل