G. Lehner

activity

20212026

collaborators

9 papers

math.AT2026

The Becker--Gottlieb transfer is not functorial: An example based on units of group rings

Georg Lehner, Cary Malkiewich, Florian Naef

We show by explicit counterexample that the Becker--Gottlieb transfer cannot be made functorial. A different counterexample using rational homotopy theory was discovered concurrent…

math.AT2026

Shape Theory of $\infty$ -Topoi: Inverse Limits, Products, and (Co)homology

Georg Lehner

We give a systematic account of the shape theory of $\infty$ -topoi, viewing the shape of an $\infty$ -topos as its generalized homotopy type. We establish the basic functorial prope…

math.KT2026

A remark on the invariance of $K$ -theory under duality

Georg Lehner

In this short remark, we explain that two examples of invariance under duality for a localizing invariant $F$ hold purely formally when $F$ is $K$ -theory, whereas the general state…

math.KT2026

Algebraic $K$ -theory of stably compact spaces

Georg Lehner

We compute the value of finitary localizing invariants, including algebraic $K$ -theory, on categories of sheaves over stably locally compact spaces $X$ . Our formula simultaneously…

math.GN2025

Measure theory via Locales

Georg Lehner

We present an approach to measure theory using the theory of locales. This includes concrete constructions of measure algebras associated to Radon measures, such as the Lebesgue me…

math.KT2025

Algebraic $K$ -theory of coherent spaces

Georg Lehner

We give a description of the value of a finitary localizing invariant, such as algebraic $K$ -theory, on the category of sheaves on a locally coherent space $X$ . This in particular…

math.KT2024

Computing the negative $K$ -theory of finite groups of order $\leq 100$

Georg Lehner

We outline how the group $K_{- 1} (Z [G])$ for a finite group $G$ can be computed using the computer language $G A P$ and compile a table of all groups $G$ of order less than…

math.KT2024

Group completion via the action $\infty$ -category

Georg Lehner

We give a generalization of Quillen's $S^{- 1} S$ construction for arbitrary $E_{n}$ -monoids as an $E_{n - 1}$ -monoidal $\infty$ -category and show that its realization models the group c…

math.KT2021

The passage from the integral to the rational group ring in algebraic $K$ -theory

Georg Lehner

An open question is whether the map $K_{0} Z G \to K_{0} Q G$ in reduced $K$ -theory from the integral to the rational group ring is tr…

The Becker--Gottlieb transfer is not functorial: An example based on units of group rings

Shape Theory of ∞-Topoi: Inverse Limits, Products, and (Co)homology

A remark on the invariance of K-theory under duality

Algebraic K-theory of stably compact spaces

Measure theory via Locales

Algebraic K-theory of coherent spaces

Computing the negative K-theory of finite groups of order ≤100

Group completion via the action ∞-category

The passage from the integral to the rational group ring in algebraic K-theory

Shape Theory of $\infty$ -Topoi: Inverse Limits, Products, and (Co)homology

A remark on the invariance of $K$ -theory under duality

Algebraic $K$ -theory of stably compact spaces

Algebraic $K$ -theory of coherent spaces

Computing the negative $K$ -theory of finite groups of order $\leq 100$

Group completion via the action $\infty$ -category

The passage from the integral to the rational group ring in algebraic $K$ -theory