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Modular Symbols and the Topological Nonrigidity of Arithmetic Manifolds
Author(s) -
Chang Stanley,
Weinberger Shmuel
Publication year - 2015
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21554
Subject(s) - mathematics , rank (graph theory) , homotopy , modular design , manifold (fluid mechanics) , space (punctuation) , pure mathematics , topology (electrical circuits) , algebra over a field , arithmetic , combinatorics , computer science , mechanical engineering , engineering , operating system
In this paper we address the existence of smooth manifolds proper homotopy equivalent to nonuniform arithmetic manifolds M = Γ\ G / K that are not homeomorphic to it. While the manifolds M are properly rigid if rank ℚ (Γ) ≤ 2, we show that the so‐called virtual structure group has infinite rank as a ℚ‐vector space if rank ℚ (Γ) ≥ 4.© 2015 Wiley Periodicals, Inc.