The gluing problem in the fusion systems of the symmetric, alternating and linear groups

Assaf Libman

doi:10.1016/j.jalgebra.2011.06.007

The gluing problem in the fusion systems of the symmetric, alternating and linear groups

Assaf Libman

Mathematical Science

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4 Citations (Scopus)

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Abstract

A solution to Linckelmann's gluing problem in all fusion systems of blocks yields an alternative formulation of Alperin's weight conjecture. Using Bredon equivariant cohomology techniques we solve the gluing problem in fusion systems (of blocks) which are isomorphic to the fusion systems of the symmetric groups or the alternating groups or $GL_d(q)$ or $SL_d(q)$ at the defining characteristic.

Original language	English
Pages (from-to)	209-245
Number of pages	37
Journal	Journal of Algebra
Volume	341
Issue number	1
Early online date	23 Jun 2011
DOIs	https://doi.org/10.1016/j.jalgebra.2011.06.007
Publication status	Published - 1 Sept 2011

Keywords

equivariant homotopy theory
gluing problem
Alperin's conjecture
radical subgroups
permutation groups

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10.1016/j.jalgebra.2011.06.007

The gluing problem in the fusion systems of the symmetric, alternating and linear groups
NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Algebra. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in JOURNAL OF ALGEBRA, [VOL 341, ISSUE 1, (2011)] DOI: 10.1016/j.jalgebra.2011.06.007
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Cite this

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AB - A solution to Linckelmann's gluing problem in all fusion systems of blocks yields an alternative formulation of Alperin's weight conjecture. Using Bredon equivariant cohomology techniques we solve the gluing problem in fusion systems (of blocks) which are isomorphic to the fusion systems of the symmetric groups or the alternating groups or $GL_d(q)$ or $SL_d(q)$ at the defining characteristic.

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KW - gluing problem

KW - Alperin's conjecture

KW - radical subgroups

KW - permutation groups

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The gluing problem in the fusion systems of the symmetric, alternating and linear groups

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