Related papers: Higher real K-theories and topological automorphic…

Quivers (directed graphs) and species (a generalization of quivers) and their representations play a key role in many areas of mathematics including combinatorics, geometry, and algebra. Their importance is especially apparent in their…

We prove a version of Quillen's stratification theorem in equivariant homotopy theory for a finite group $G$, generalizing the classical theorem in two directions. Firstly, we work with arbitrary commutative equivariant ring spectra as…

We prove the Farrell-Jones Isomorphism Conjecture about the algebraic K-theory of a group ring RG in the case where the group G is the fundamental group of a closed Riemannian manifold with strictly negative sectional curvature. The…

Let $k$ be an algebraically closed field of positive characteristic $p$ and let $\mathbb{G}_a$ denote the additive group of $k$. Let $n \geq 1$ and let ${\rm Mat}(n, k[T])^E$ denote the set of all exponential matrices of ${\rm Mat}(n,…

We give a survey of several models of irreducible complementary series representations and their limits, special representations, for the groups SU(n,1) and SO(n,1), including new ones. These groups, whose geometrical meaning is well known,…

This project considers the finite symmetry subgroups of the orthogonal group $\mathrm{O}(3) \subset \mathrm{GL}(3,\mathbb{R})$ and the index $2$ containments $G\lhd \widehat{G}$. The special orthogonal group $\mathrm{SO}(3) \subset…

In recent work, we related the structure of subvarieties of $n\times n$ complex matrices defined by eigenvalue coincidences to $GL(n-1,\mathbb{C})$-orbits on the flag variety of $\mathfrak{gl}(n,\mathbb{C})$. In the first part of this…

The relative Novikov conjecture states that the relative higher signatures of manifolds with boundary are invariant under orientation-preserving homotopy equivalences of pairs. In this paper, we study the relative Baum-Connes assembly map…

Let $k$ be a field of characteristic zero and let $(F,R)$ be a Landweber exact formal group law. We consider a Landweber exact $T$-spectrum $\mathcal{E}:=R\otimes_{\mathbb{L}}\text{MGL}$ and its effective cover $f_0\mathcal{E}\to…

Let E_n be the Lubin-Tate spectrum and let G_n be the nth extended Morava stabilizer group. Then there is a discrete G_n-spectrum F_n, with L_{K(n)}(F_n) \simeq E_n, that has the property that (F_n)^{hU} \simeq E_n^{hU}, for every open…

Let $\mathfrak{o}$ be the ring of integers in a non-Archimedean local field with finite residue field, $\mathfrak{p}$ its maximal ideal, and $r\geq2$ an integer. An irreducible representation of the finite group…

Let $\mathfrak{g}$ be a finite-dimensional semisimple complex Lie algebra and $\theta$ an involutive automorphism of $\mathfrak{g}$. According to G. Letzter, S. Kolb and M. Balagovi\'c the fixed-point subalgebra $\mathfrak{k} =…

We prove that for every finitely generated subgroup of a virtually connected Lie group which admits a finite dimensional model for the classifying space for proper actions the assembly map in algebraic K-theory is split injective. We also…

We describe the construction which takes as input a profinite group, which when applied the the absolute Galois group of a geometric field F agrees in some cases with the algebraic K-theory of F. We prove that it agrees in the case of a…

We identify the $K$-theoretic fiber of a localization of ring spectra in terms of the $K$-theory of the endomorphism algebra spectrum of a Koszul-type complex. Using this identification, we provide a negative answer to a question of Rognes…

We determine the class of finite T_0-spaces allowing for a universal coefficient theorem computing equivariant KK-theory by filtrated K-theory.

We introduce uniform K-stability and its relationship with the coercivity property of the K-energy functional, for general polarized manifolds. Since the automorphism groups are not necessarily finite, size of the norm measuring uniformity…

In this note, we show how a continuous action of the Morava stabilizer group $\mathbb G_n$ on the Lubin-Tate spectrum $E_n$, satisfying the conclusion $E_n^{h\mathbb G_n}\simeq L_{K(n)} S$ of the Devinatz-Hopkins Theorem, may be obtained by…

This paper provides a comparison between the $K$-structure of unipotent representations and regular sections of bundles on nilpotent orbits for complex groups of type $D$. Precisely, let $ G_ 0 =Spin(2n,\mathbb C)$ be the Spin complex group…

In this article we describe the $G_{comp}\times G_{comp}$-equivariant topological $K$-ring of a {\em cellular} toroidal embedding $\mathbb{X}$ of a complex connected reductive algebraic group $G$. In particular, our results extend the…