TY - JOUR
T1 - Mapping class group actions on configuration spaces and the Johnson filtration
AU - Bianchi, Andrea
AU - Miller, Jeremy
AU - Wilson, Jennifer C.H.
N1 - Publisher Copyright:
© 2022 American Mathematical Society.
PY - 2022
Y1 - 2022
N2 - Let Fn(Σg,1) denote the configuration space of n ordered points on the surface Σg,1 and let Γg,1 denote the mapping class group of Σg,1. We prove that the action of Γg,1 on Hi(Fn(Σg,1); ℤ) is trivial when restricted to the ith stage of the Johnson filtration J(i) ⊂ Γg,1. We give examples showing that J(2) acts nontrivially on H3(F3(Σg,1)) for g ≥ 2, and provide two new conceptual reinterpretations of a certain group introduced by Moriyama.
AB - Let Fn(Σg,1) denote the configuration space of n ordered points on the surface Σg,1 and let Γg,1 denote the mapping class group of Σg,1. We prove that the action of Γg,1 on Hi(Fn(Σg,1); ℤ) is trivial when restricted to the ith stage of the Johnson filtration J(i) ⊂ Γg,1. We give examples showing that J(2) acts nontrivially on H3(F3(Σg,1)) for g ≥ 2, and provide two new conceptual reinterpretations of a certain group introduced by Moriyama.
UR - http://www.scopus.com/inward/record.url?scp=85137540282&partnerID=8YFLogxK
U2 - 10.1090/tran/8637
DO - 10.1090/tran/8637
M3 - Journal article
AN - SCOPUS:85137540282
VL - 375
SP - 5461
EP - 5489
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 8
ER -