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Cat(0) Groups with Non‐Locally Connected Boundary
Author(s) -
Mihalik Michael,
Ruane Kim
Publication year - 1999
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/s0024610799008030
Subject(s) - boundary (topology) , mathematics , coxeter group , space (punctuation) , group (periodic table) , simply connected space , variety (cybernetics) , pure mathematics , locally compact space , construct (python library) , topology (electrical circuits) , combinatorics , mathematical analysis , computer science , physics , statistics , quantum mechanics , operating system , programming language
The main theorem shows that whenever certain amalgamated products act geometrically on a CAT(0) space, the space has non‐locally connected boundary. One can now easily construct a wide variety of examples of one‐ended CAT(0) groups with non‐locally connected boundary. Applications of this theorem to right‐angled Coxeter and Artin groups are considered. In particular, it is shown that the natural CAT(0) space on which a right‐angled Artin group acts has locally connected boundary if and only if the group is Z n for some n .