E∞ -cells and general linear groups of finite fields

Soren GALATIUS; Alexander Kupers; Oscar RANDAL-WILLIAMS

doi:10.17863/cam.124922

January 23, 2025Open Access

E∞ -cells and general linear groups of finite fields

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Key Points

The study aims to establish new homological stability results for general linear groups over finite fields.
Constructed CW approximations to classifying spaces of general linear groups.
Utilized E∞-algebras to guide the construction.
Performed homology computations with coefficients in the E1-split Steinberg module.
New homological stability results confirmed for general linear groups over finite fields.
Construction of CW approximations led to significant insights into group properties.

Implication

New results demonstrate homological stability in finite field linear groups, indicating important algebraic properties.

Abstract

We prove new homological stability results for general linear groups over finite fields. These results are obtained by constructing CW approximations to the classifying spaces of these groups, in the category ofE∞ -algebras, guided by computations of homology with coefficients in theE1-split Steinberg module.

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Cite This Study

GALATIUS et al. (2025) studied this question.

synapsesocial.com/papers/6971bea8642b1836717e34c5 https://doi.org/10.17863/cam.124922

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E∞ -cells and general linear groups of finite fields

Key Points

Implication

Abstract

Discussion

Cite This Study

E∞ -cells and general linear groups of finite fields

Key Points

Implication

Abstract

Discussion

Cite This Study

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