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2014 The thick-thin decomposition and the bilipschitz classification of normal surface singularities
Lev Birbrair, Walter D. Neumann, Anne Pichon
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Acta Math. 212(2): 199-256 (2014). DOI: 10.1007/s11511-014-0111-8


We describe a natural decomposition of a normal complex surface singularity (X, 0) into its “thick” and “thin” parts. The former is essentially metrically conical, while the latter shrinks rapidly in thickness as it approaches the origin. The thin part is empty if and only if the singularity is metrically conical; the link of the singularity is then Seifert fibered. In general the thin part will not be empty, in which case it always carries essential topology. Our decomposition has some analogy with the Margulis thick-thin decomposition for a negatively curved manifold. However, the geometric behavior is very different; for example, often most of the topology of a normal surface singularity is concentrated in the thin parts.

By refining the thick-thin decomposition, we then give a complete description of the intrinsic bilipschitz geometry of (X, 0) in terms of its topology and a finite list of numerical bilipschitz invariants.


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Lev Birbrair. Walter D. Neumann. Anne Pichon. "The thick-thin decomposition and the bilipschitz classification of normal surface singularities." Acta Math. 212 (2) 199 - 256, 2014.


Received: 19 January 2012; Revised: 21 June 2013; Published: 2014
First available in Project Euclid: 30 January 2017

zbMATH: 1303.14016
MathSciNet: MR3207758
Digital Object Identifier: 10.1007/s11511-014-0111-8

Primary: 14B05
Secondary: 32S05 , 32S25 , 57M99

Keywords: bilipschitz geometry , normal surface singularity , thick-thin decomposition

Rights: 2014 © Institut Mittag-Leffler

Vol.212 • No. 2 • 2014
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