The pure symmetric automorphisms of a free group form a duality group

DOI10.1006/jabr.2001.8941zbMath0995.20010OpenAlexW2078012663MaRDI QIDQ5957540

Noel Brady, Jon McCammond, John Meier, Andy Miller

Publication date: 2 July 2002

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.2001.8941

zbMATH Keywords

dualityautomorphism groupslinksfree groupsfinite posetsCohen-Macaulay posetscontractible simplicial complexesduality groupspure symmetric automorphismsrecursive atom orderingsshellable posets

Mathematics Subject Classification ID

Automorphism groups of groups (20F28) Free nonabelian groups (20E05)

Related Items

Automorphisms of free groups with boundaries., A note on virtual duality and automorphism groups of right-angled Artin groups, Representation stability for the cohomology of the pure string motion groups., Action of the symmetric groups on the homology of the hypertree posets, Euler classes and Bredon cohomology for groups with restricted families of finite subgroups., Symmetric automorphisms of free groups, BNSR-invariants, and finiteness properties, Finiteness properties for a subgroup of the pure symmetric automorphism group., The integral cohomology of the group of loops., Representations of pure symmetric automorphism groups of RAAGs

Cites Work

• Unnamed Item
• Unnamed Item
• Cohomological dimension and symmetric automorphisms of a free group
• The theory of motion groups
• Improper actions and higher connectivity at infinity
• The topology at infinity of \(\text{Out} (F_n)\)
• Groups with homological duality generalizing Poincaré duality
• On Lexicographically Shellable Posets
• Shellable and Cohen-Macaulay Partially Ordered Sets
• Normal Forms for Basis-Conjugating Automorphisms of a Free Group
• Symmetric automorphisms of free products
• The Bieri-Neumann-Strebel invariant for basis-conjugating automorphisms of free groups