The integral cohomology of the group of loops
By C. Jensen, Jon McCammond, John Meier. 2006
54 citations recorded by the source corpus.
Let PSigma_n denote the group that can be thought of either as the group of motions of the trivial n-component link or the group of symmetric automorphisms of a free group of rank n. The integral cohomology ring of PSigma_n is determined, establishing a conjecture of Brownstein and Lee.
Subfields: Geometry and Topology, Theoretical Computer Science
View Paper: https://www.semanticscholar.org/paper/6cf7b2708af3be41c8193c9d0d82a5e392103520
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In Geometry and Topology
- Jenny Wilson
- Nathalie Wahl
- Tara E. Brendle
- A. Hatcher
- Benson Farb
- O. Randal-Williams
- C. Damiani
- Søren Galatius
In Theoretical Computer Science
Citations in the corpus
- Representation theory and homological stability (2010, unknown): “n is the space of nunordered unoriented unlinked loops, and its fundamental group BΣ n:= π1(Y′′) is the group of string motions. The cohomology ring of PΣn has been computed by Jensen–McCammond–Meier [JMM], who prove that H∗(PΣn;Q) is generated by classes αij ∈H1(PΣn;Q) for all i6= j, 1 ≤i,j≤n, subj”
- Configuration spaces of rings and wickets (2008, result): “Other references are [G], [BL], [R], [BMMM], [ JMM ],”
- Representation stability for the cohomology of the pure string motion groups (2011, methodology): “It has been studied by Collins [7], Brownstein and Lee [5], Brady, McCammond, Meier and Miller [2], Pettet [20], Jensen, McCammond and Meier [17] and others.”
- FI_W-modules and stability criteria for representations of the classical Weyl groups (2013, methodology): “In [Wil12], to prove that the sequenceH(PΣn;Q) is uniformly representation stable, we use a combinatorial description of the cohomology groups given by Jensen–McCammond–Meier [JMM06] and an orbit–stabilizer argument to decompose each group into a sum of induced representation of a particular form.”
- Stabilization for mapping class groups of 3-manifolds (2007, background): “The stabilization ΣAut(Fn) → ΣAut(Fn+1) induces an isomorphism on Hi for n ≥ 2i+ 2 and a surjection for n = 2i+ 1.”