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Strong Jordan Separation and Applications to Rigidity
Author(s) -
Lafont Jean-François
Publication year - 2006
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/s0024610706022745
Subject(s) - rigidity (electromagnetism) , injective function , mathematics , pure mathematics , structural rigidity , mathematical analysis , combinatorics , physics , quantum mechanics
We prove that simple, thick hyperbolic P‐manifolds of dimension at least three exhibit Mostow rigidity. We also prove a quasi‐isometry rigidity result for the fundamental groups of simple, thick hyperbolic P‐manifolds of dimension at least three. The key tool in the proof of these rigidity results is a strong form of the Jordan separation theorem, for maps from S n → S n +1 which are not necessarily injective.