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pro vyhledávání: '"Wilson, Jennifer C. H."'
In this paper, we study sequences of topological spaces called "vertical configuration spaces" of points in Euclidean space. We apply the theory of FI$_G$-modules, and results of Bianchi-Kranhold, to show that their (co)homology groups are "represent
Externí odkaz:
http://arxiv.org/abs/2412.01128
Motivated by his work on the stable rank filtration of algebraic K-theory spectra, Rognes defined a simplicial complex called the common basis complex and conjectured that this complex is highly connected for local rings and Euclidean domains. We pro
Externí odkaz:
http://arxiv.org/abs/2303.00245
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
We survey stability properties of several families of moduli spaces, with a focus on braid groups and configuration spaces.
Comment: Minor corrections and updated references. To appear in the Notices of the American Mathematical Society. This ve
Comment: Minor corrections and updated references. To appear in the Notices of the American Mathematical Society. This ve
Externí odkaz:
http://arxiv.org/abs/2201.04096
Let $F_n(\Sigma_{g,1})$ denote the configuration space of $n$ ordered points on the surface $\Sigma_{g,1}$ and let $\Gamma_{g,1}$ denote the mapping class group of $\Sigma_{g,1}$. We prove that the action of $\Gamma_{g,1}$ on $H_i(F_n(\Sigma_{g,1});\
Externí odkaz:
http://arxiv.org/abs/2104.09253
Publikováno v:
IMRN (2022), no. 13, 10347-10401
We study presentations of the virtual dualizing modules of special linear groups of number rings, the Steinberg modules. Bykovskii gave a presentation for the Steinberg modules of the integers, and our main result is a generalization of this presenta
Externí odkaz:
http://arxiv.org/abs/2006.10906
Autor:
Miller, Jeremy, Wilson, Jennifer C. H.
Using a result of Gan and Li on FI-hyperhomology and a semi-simplicial resolution of configuration spaces due to Randal-Williams, we establish an improved representation stability stable range for configuration spaces of distinct ordered points in a
Externí odkaz:
http://arxiv.org/abs/1903.02722
Akademický článek
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Publikováno v:
J. Topol. 13 (2020), no. 2, 441-459
We prove that the Steinberg module of the special linear group of a quadratic imaginary number ring which is not Euclidean is not generated by integral apartments. Assuming the generalized Riemann hypothesis, this shows that the Steinberg module of a
Externí odkaz:
http://arxiv.org/abs/1810.07683
Autor:
Miller, Jeremy, Wilson, Jennifer C. H.
We introduce a technique for proving quantitative representation stability theorems for sequences of representations of certain finite linear groups over a field of characteristic zero. In particular, we prove a vanishing result for higher syzygies o
Externí odkaz:
http://arxiv.org/abs/1709.03638