Non-trivial action of the Johnson filtration on the homology of configuration spaces

2022/08/02 by Bianchi, Andrea, Stavrou, Andreas · 2 citations
#55R80 #57K20 #Algebraic Topology (math.AT) #FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2208.01608

Abstract

We let the mapping class group Γ_g,1 of a genus g surface Σ_g,1 with one boundary component act on the homology H_*(F_n(Σ_g,1);ℚ) of the n^th ordered configuration space of the surface. We prove that the action is non-trivial when restricted to the (n-1)^st stage of the Johnson filtration, for all n≥ 1 and g≥ 2. We deduce an analogous result for closed surfaces.

Cited by

• Surface configuration kernels
• The configuration functor of a punctured space

Related

• Mapping class group actions on configuration spaces and the Johnson filtration
• Surface configuration kernels
• Homological stability for quotients of mapping class groups of surfaces by the Johnson subgroups
• Decoupling generalised configuration spaces on surfaces
• Surface Homeomorphisms That Do Not Extend to Any Handlebody and the Johnson Filtration