Asymptotic dimension of proper CAT(0) spaces which are homeomorphic to the plane

2008/11/09 by Naotsugu Chinen, Chinen, Naotsugu, Tetsuya Hosaka +1
Mathematics · #20F65 #20F69 #54F45 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT #msc:20F65 #msc:20F69 #msc:54F45

paper · pdf · doi:10.48550/arxiv.0811.1325

arxiv created 2008/11/09 · arxiv updated 2009/12/01

Abstract

In this paper, we investigate a proper CAT(0) space (X,d) which is homeomorphic to R² and we show that the asymptotic dimension asdim (X,d) is equal to 2.

Related

• Asymptotic topological regularity of CAT(0) spaces
• Asymptotic dimension of planes and planar graphs
• On the capacity dimension of the boundary of CAT(0) spaces
• Universal spaces for asymptotic dimension
• Remarks on asymptotic power dimension