Premium
Homomorphisms From Mapping Class Groups
Author(s) -
Harvey William J.,
Korkmaz Mustafa
Publication year - 2005
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609304003911
Subject(s) - mathematics , homomorphism , mathematics subject classification , mapping class group , rigidity (electromagnetism) , class (philosophy) , pure mathematics , combinatorics , algebra over a field , geometry , artificial intelligence , surface (topology) , computer science , structural engineering , engineering
This paper concerns rigidity of the mapping class groups. It is shown that any homomorphism ϕ : Mod g → Mod h between mapping class groups of closed orientable surfaces with distinct genera g > h is trivial if g ⩾ 3, and has finite cyclic image for all g ⩾ 1. Some implications are drawn for more general homomorphs of these groups. 2000 Mathematics Subject Classification 57N05 (primary), 20E25, 30F10 (secondary).