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Fundamental pro‐groups and Gromov boundaries of 7‐systolic groups
Author(s) -
Świątkowski Jacek
Publication year - 2009
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/jdp047
Subject(s) - mathematics , class (philosophy) , property (philosophy) , pure mathematics , metric (unit) , dimension (graph theory) , metric space , group (periodic table) , fundamental group , saturation (graph theory) , topology (electrical circuits) , computer science , combinatorics , physics , business , artificial intelligence , philosophy , epistemology , marketing , quantum mechanics
We introduce the property of pro‐π 1 ‐saturation (defined in terms of fundamental pro‐groups) for compact metric spaces. We expect (though cannot yet prove) this property to be stronger than hereditary asphericity. We show that 1‐dimensional spaces and Gromov boundaries of 7‐systolic groups are pro‐π 1 ‐saturated (the latter class contains examples of pro‐π 1 ‐saturated spaces with arbitrary finite topological dimension).