Related papers: Mackey profunctors
We extend the theory of Mackey 2-functors introduced in arXiv:1808.04902 by defining the appropriate notion of rings, namely Green 2-functors. After providing the first results of our theory and abundant examples, we show how all classical…
Surface groups are determined among limit groups by their profinite completions. As a corollary, the set of surface words in a free group is closed in the profinite topology.
We define and investigate the concept of the groupoid representation induced by a representation of the isotropy subgroupoid. Groupoids in question are locally compact transitive topological groupoids. We formulate and prove the…
We prove the Milnor conjecture for Lie groups and the Friedlander conjecture for complex algebraic Lie groups.
The Profinite Isomorphism Problem for a class of groups \mathcal{C} asks for an algorithm that decides for any two groups in \mathcal{C} whether they have isomorphic profinite completions. We present the positive solution to this problem…
We construct an algebraic homology functor for Artin stacks of finite type over a field, and we develop intersection-theoretic properties.
We introduce the class of projective reflection groups which includes all complex reflection groups. We show that several aspects involving the combinatorics and the representation theory of all non exceptional irreducible complex…
In this paper we formulate a conjecture which is a strengthening of an extension theorem of Bakonyi and Timotin for positive definite functions on the free group on two generators. We prove that this conjecture implies Connes' embedding…
We apply Mackey procedure of classifying projective systems of imprimitivity to a thorough study of the projective unitary irreducible representations of the Galilei group in 1+3 and 1+2 dimensions.
We prove that every small profinite group can be decomposed into a direct product of indecomposable profinite groups, and that such a decomposition is unique up to order and isomorphisms of the components. We also investigate the…
Symmetric cohomology of groups, defined by M. Staic in [2], is similar to the way one defines the cyclic cohomology for algebras. We show that there is a well-defined restriction, conjugation and transfer map in symmetric cohomology, which…
We introduce endo-permutation Mackey functors and the Mackey-Dade group of a $p$-group and study their basic properties. We exhibit relations between the Mackey-Dade group of a finite $p$-group $P$ and the Dade groups of the Weyl groups of…
For a finite group $G$, the so-called $G$-Mackey functors form an abelian category $M(G)$ that has many applications in the study of $G$-equivariant stable homotopy. One would expect that the derived category $D(M(G))$ would be similarly…
In this note, we extend the inductions and restrictions of modules over finite groups to non-injective group homomorphisms, establishing transitivity, Frobenius reciprocity, Mackey's formula, etc.
In this work we introduce reciprocity functors, construct the associated K-group of a family of reciprocity functors, which itself is a reciprocity functor, and compute it in several different cases. It may be seen as a first attempt to get…
Certain classical generating functions for elements of reflection groups can be expressed using fundamental invariants called exponents. We give new analogues of such generating functions that accommodate orbits of reflecting hyperplanes…
We exhibit gluing properties of cluster tilting subcategories in exact $\infty$-categories within the framework of perverse schobers on surfaces with boundary. These results are based on a study of the restriction functors from global…
Broadly speaking, a finiteness property of groups is any generalisation of the property of having finite order. A large part of infinite group theory is concerned with finiteness properties and the relationships between them. Profinite…
In this work we extend the Mackey's theory of induced unitary representations on a wide class of Krein-isometric induced representations in Krein spaces. The subgroup theorem and the Kronecker product theorem are shown to be valid for the…
Let G be a finite group. We systematically exploit general homological methods in order to reduce the computation of G-equivariant KK-theory to topological equivariant K-theory. The key observation is that the functor assigning to a…