Related papers: Homology decompositions and groups inducing fusion…

Geometry of buildings is used to prove some homological properties of the category of smooth representations of a reductive p-adic group (Kazhdan's "pairing conjecture", Bernstein's description of homological duality in terms of…

We prove that an isomorphism between saturated fusion systems over the same finite p-group is detected on the elementary abelian subgroups of the hyperfocal subgroup if p is odd, and on the abelian subgroups of the hyperfocal subgroup of…

The assignment of classifying spectra to saturated fusion systems was suggested by Linckelmann and Webb and has been carried out by Broto, Levi and Oliver. A more rigid (but equivalent) construction of the classifying spectra is given in…

We introduce a functional realization of the Hamiltonian structure on the moduli space of P-bundles on the elliptic curve E. Here P is parabolic subgroup in SL_n. We also introduce a construction of the corresponding quantum algebras.

Let $G$ be a group which admits the structure of an iterated semidirect product of finitely generated free groups. We construct a finite, free resolution of the integers over the group ring of $G$. This resolution is used to define…

This manuscript represents the author's PhD dissertation thesis.The first part studies decision problems in Thompson's groups F,T,V and some generalizations. The simultaneous conjugacy problem is determined to be solvable for Thompson's…

We show that a finite collection of stable subgroups of a finitely generated group has finite height, finite width and bounded packing. We then use knowledge about intersections of conjugates to characterize finite families of…

Suppose $G$ is a locally solid lattice group. It is known that there are non-equivalent classes of bounded homomorphisms on $G$ which have topological structures. In this paper, our attempt is to assign lattice structures on them. More…

We present definitions of homology groups associated to a family of amalgamation functors. We show that if the generalized amalgamation properties hold, then the homology groups are trivial. We compute the group H_2 for strong types in…

We prove that homological filling functions over a ring $R$ equipped with the discrete norm are quasi-isometry invariants for all groups of type $\mathrm{FP}_n$. This confirms a conjecture of Bader-Kropholler-Vankov in the case of discrete…

We define a `tree of fusion systems' and give a sufficient condition for its completion to be saturated. We apply this result to enlarge an arbitrary fusion system by extending the automorphism groups of certain of its subgroups.

The existence of ring-like structures in exact hopfion solutions is shown.

The subject of the present work is the de Rham part of non-commutative Hodge structures on the periodic cyclic homology of differential graded algebras and categories. We discuss explicit formulas for the corresponding connection on the…

By studying cohomology classes that are related with $p$-harmonic morphisms, $F$-harmonic maps, and $f$-harmonic maps, we extend several of our previous results on Riemannian submersions and $p$-harmonic morphisms to $F$-harmonic maps, and…

We examine the cohomology and representation theory of a family of finite supergroup schemes of the form $(\mathbb G_a^-\times \mathbb G_a^-)\rtimes (\mathbb G_{a(r)}\times (\mathbb Z/p)^s)$. In particular, we show that a certain relation…

Let G be a group and H be a Hartley set of G. In this paper, we prove the existence and conjugacy of H-injectors of G and describe the structure of the injectors. As application, some known results are directly followed.

In this paper we first survey some basic results in the cohomology of finite groups, and then discuss recent work on constructing free actions of finite groups on products of spheres.

We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.

This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…

In the early 1980s Ross Geoghegan and I calculated the homology of Richard Thompson's group F as a graded abelian group. It turns out that the homology admits a natural ring structure, which I calculate in this paper. As a byproduct, I…