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o‐Minimal Fundamental Group, Homology and Manifolds
Author(s) -
Berarducci Alessandro,
Otero Margarita
Publication year - 2002
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/s0024610701003015
Subject(s) - mathematics , fundamental group , homology (biology) , realization (probability) , manifold (fluid mechanics) , pure mathematics , simplicial complex , group (periodic table) , dimension (graph theory) , topology (electrical circuits) , combinatorics , physics , chemistry , gene , mechanical engineering , biochemistry , statistics , quantum mechanics , engineering
The definable fundamental group of a definable set in an o‐minimal expansion of a field is computed. This is achieved by proving the relevant case of the o‐minimal van Kampen theorem. This result is applied to show that if the geometrical realization of a simplicial complex over an o‐minimal expansion of a field is a definable manifold of dimension not 4, then its geometrical realization over the reals is a topological manifold.