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

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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 languageEnglish
Pages (from-to)209-245
Number of pages37
JournalJournal of Algebra
Volume341
Issue number1
Early online date23 Jun 2011
DOIs
Publication statusPublished - 1 Sep 2011

Keywords

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

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