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Non‐Free Points for Groups Generated by a Pair of 2×2 Matrices
Author(s) -
Bamberg John
Publication year - 2000
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610700001630
Subject(s) - mathematics , symmetry (geometry) , point (geometry) , combinatorics , free group , plane (geometry) , group (periodic table) , free form , free product , pure mathematics , plane symmetry , relation (database) , geometry , physics , computer science , quantum mechanics , computer graphics (images) , database
A point λ in the complex plane is said to be free if the group generated by the matrices(1 20 1)and(1 0λ 1)is free. The paper gives an infinite family of polynomials whose roots are the non‐free points. The main idea in the paper is to employ a symmetry relation.