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pro vyhledávání: '"Brück, Benjamin"'
Autor:
Brück, Benjamin
Church-Farb-Putman formulated stability and vanishing conjectures for the high-dimensional cohomology of $\operatorname{SL}_n(\mathbb{Z})$, surface mapping class groups and automorphism groups of free groups. This is a survey on the current status of
Externí odkaz:
http://arxiv.org/abs/2404.15026
For a finite-dimensional vector space $V$, the common basis complex of $V$ is the simplicial complex whose vertices are the proper non-zero subspaces of $V$, and $\sigma$ is a simplex if and only if there exists a basis $B$ of $V$ that contains a bas
Externí odkaz:
http://arxiv.org/abs/2402.10484
Autor:
Brück, Benjamin, Himes, Zachary
Let $K$ be a number field with ring of integers $R = \mathcal{O}_K$. We show that if $R$ is not a principal ideal domain, then the symplectic group $\operatorname{Sp}_{2n}(R)$ has non-trivial rational cohomology in its virtual cohomological dimension
Externí odkaz:
http://arxiv.org/abs/2309.05456
We compute the weight 2 cohomology of the Feynman transforms of the cyclic (co)operads $\mathsf{BV}$ and $\mathsf{HyCom}$, and the top$-2$ weight cohomology of the Feynman transforms of $D\mathsf{BV}$ and $\mathsf{Grav}$. Using a result of Giansiracu
Externí odkaz:
http://arxiv.org/abs/2308.16845
Borel-Serre proved that the integral symplectic group $\operatorname{Sp}_{2n}(\mathbb{Z})$ is a virtual duality group of dimension $n^2$ and that the symplectic Steinberg module $\operatorname{St}^\omega_n(\mathbb{Q})$ is its dualising module. This m
Externí odkaz:
http://arxiv.org/abs/2306.03180
Autor:
Brück, Benjamin, Sroka, Robin J.
In this note we present an alternative proof of a theorem of Gunnells, which states that the Steinberg module of $\operatorname{Sp_{2n}}(\mathbb{Q})$ is a cyclic $\operatorname{Sp_{2n}}(\mathbb{Z})$-module, generated by integral apartment classes.
Externí odkaz:
http://arxiv.org/abs/2305.17697
Let $\mathbb{K}$ be a number field with ring of integers $\mathfrak{O}$ and let $\mathcal{G}$ be a Chevalley group scheme not of type $\mathtt{E}_8$, $\mathtt{F}_4$ or $\mathtt{G}_2$. We use the theory of Tits buildings and a result of T\'oth on Stei
Externí odkaz:
http://arxiv.org/abs/2210.12784
Cup products provide a natural approach to access higher bounded cohomology groups. We extend vanishing results on cup products of Brooks quasimorphisms of free groups to cup products of median quasimorphisms, i.e., Brooks-type quasimorphisms of grou
Externí odkaz:
http://arxiv.org/abs/2209.05811
Borel-Serre proved that $\mathrm{SL}_n(\mathbb{Z})$ is a virtual duality group of dimension $n \choose 2$ and the Steinberg module $\mathrm{St}_n(\mathbb{Q})$ is its dualizing module. This module is the top-dimensional homology group of the Tits buil
Externí odkaz:
http://arxiv.org/abs/2204.11967
Autor:
Heydenreich, Sven, Brück, Benjamin, Burger, Pierre, Harnois-Déraps, Joachim, Unruh, Sandra, Castro, Tiago, Dolag, Klaus, Martinet, Nicolas
Publikováno v:
A&A 667, A125 (2022)
We demonstrate how to use persistent homology for cosmological parameter inference in a tomographic cosmic shear survey. We obtain the first cosmological parameter constraints from persistent homology by applying our method to the first-year data of
Externí odkaz:
http://arxiv.org/abs/2204.11831