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A note on Trace‐Fields of Kleinian Groups
Author(s) -
Reid Alan W.
Publication year - 1990
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/blms/22.4.349
Subject(s) - commensurability (mathematics) , corollary , mathematics , confusion , invariant (physics) , pure mathematics , class (philosophy) , mathematical physics , psychology , epistemology , philosophy , psychoanalysis
Let Γ Kleinian group of finite covolume. In the past there seems to have been some confusion as to whether the trace‐field of Γ is an invariant of the commensurability class of Γ. In fact, when Γ is arithmetic this is known not to be the case. Here we clear up this confusion in general by producing a field which is an invariant of the commensurability class. As an elementary corollary it then follows that there exist infinitely many commensurability classes of closed hyperbolic 3‐manifolds which fibre over the circle.