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Limits of topological minimal sets with finitely generated coefficient groups
Author(s) -
Liang Xiangyu
Publication year - 2016
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/jlms/jdw028
Subject(s) - mathematics , homology (biology) , finitely generated abelian group , singular homology , hausdorff space , pure mathematics , topology (electrical circuits) , combinatorics , biology , biochemistry , gene
We prove that the (local) Hausdorff limit of topological minimal sets (with finitely generated coefficient group) is topologically minimal. The key idea is to reduce the homology group on the space to the homology group on the sphere, and then reduce the homology group on the sphere to a finitely representable one, by ‘glueing’ grids with small measure to block local elements in the homology group.