CAT(0) spaces and expanders

We construct a CAT(0) space Y with Izeki–Nayatani invariant δ ( Y ) = 1. By a similar construction, we also prove that there exists a CAT(0) space which does not have Markov type p for every p  > 1.

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Bibliographic Details
Published inMathematische Zeitschrift Vol. 271; no. 1-2; pp. 343 - 355
Main Author Kondo, Takefumi
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.06.2012
Subjects
Mathematics
Mathematics and Statistics
CAT space
Primary 20F65
Izeki–Nayatani invariant
Markov type
Spectral gap
Secondary 58E20
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Summary:We construct a CAT(0) space Y with Izeki–Nayatani invariant δ ( Y ) = 1. By a similar construction, we also prove that there exists a CAT(0) space which does not have Markov type p for every p  > 1.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-011-0866-y