Related papers: Evaluation maps and transfers for free loop spaces…
Simplicial formal maps were introduced in the first paper, (math.QA/0512032), of this series as a tool for studying Homotopy Quantum Field Theories with background a general homotopy 2-type. Here we continue their study, showing how a…
Given a fibration of simply connected CW complexes of finite type, we study the evaluation subgroup of the fibre inclusion as an invariant of fibre-homotopy type. For spherical fibrations, we show the evaluation subgroup may be expressed as…
We obtain a complete classification of all finite-dimensional irreducible modules over classical map superalgebras, provide formulas for their (super)characters and a description of their extension groups. Furthermore, we describe the block…
Given a locally presentable category together with a suitable functorial cylinder object, we construct model structures which are sensitive to the `direction' of the cylinder. We show that the Covariant and Contravariant model structures on…
The theory of p-local compact groups, developed in an earlier paper by the same authors, is designed to give a unified framework in which to study the p-local homotopy theory of classifying spaces of compact Lie groups and p-compact groups,…
According to the Langlands functoriality conjecture, broadened to the setting of spherical varieties (of which reductive groups are special cases), a map between L-groups of spherical varieties should give rise to a functorial transfer of…
The bootstrap category in E-theory for C*-algebras over a finite space X is embedded into the homotopy category of certain diagrams of K-module spectra. Therefore it has infinite n-order for every n. The same holds for the bootstrap…
We develop model categories of rational equivariant spectra whose homotopy categories are equivalent to the category of rational equivariant cohomology theories. We prove that given an orthogonal decomposition of the unit in the rational…
We show that the functor which assigns to an A-infinity morphism between isotopy classes of A-infinity algebras whose linear part is a chain homotopy equivalence its underlying chain map is a discrete Grothendieck bifibration. We then…
Natural linear and coalgebra transformations of tensor algebras are studied. The representations of certain combinatorial groups are given. These representations are connected to natural transformations of tensor algebras and to the groups…
Let $F$ be a local field with residue field $k$. The classifying space of $GL_n(F)$ comes canonically equipped with a map to the delooping of the $K$-theory space of $k$. Passing to loop spaces, such a map abstractly encodes a homotopy…
In paper arXiv:1406.1744, we constructed a symmetric monoidal category $LIE^{MC}$ whose objects are shifted (and filtered) L-infinity algebras. Here, we fix a cooperad $C$ and show that algebras over the operad $Cobar(C)$ naturally form a…
We prove that one can realize certain triangulated subcategories of the singularity category of a complete intersection as homotopy categories of matrix factorizations. Moreover, we prove that for any commutative ring and non-zerodivisor,…
We explicitly determine the spectrum of transfer operators (acting on spaces of holomorphic functions) associated to analytic expanding circle maps arising from finite Blaschke products. This is achieved by deriving a convenient natural…
The results of a previous paper on the equivariant homotopy theory of crossed complexes are generalised from the case of a discrete group to general topological groups. The principal new ingredient necessary for this is an analysis of…
In this article, we establish the compatibility between norms and transfers in motivic homotopy theory. More precisely, we construct norm functors for motivic spaces equipped with various flavours of transfer. This yields a norm monoidal…
The classifying space of a crossed complex generalises the construction of Eilenberg-Mac Lane spaces. We show how the theory of fibrations of crossed complexes allows the analysis of homotopy classes of maps from a free crossed complex to…
We present an intrinsic and concrete development of the subdivision of small categories, give some simple examples and derive its fundamental properties. As an application, we deduce an alternative way to compare the homotopy categories of…
The Segal map connects the Burnside category of finite groups to the stable homotopy category of their classifying spaces. The chromatic filtrations on the latter can be used to define filtrations on the former. We prove a related…
Let $\mathcal{E}(X)$ be the group of homotopy classes of self homotopy equivalences for a connected CW complex $X$. We observe two classes of maps $\mathcal{E}$-maps and co-$\mathcal{E}$-maps. They are defined as the maps $X\to Y$ that…