Abstract
We show that a weighted homogeneous complex surface singularity is metrically conical (i.e., bi-Lipschitz equivalent to a metric cone) only if its two lowest weights are equal. We also give an example of a pair of weighted homogeneous complex surface singularities that are topologically equivalent but not bi-Lipschitz equivalent.
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Birbrair, L., Fernandes, A.: Metric geometry of complex algebraic surfaces with isolated singularities. Comm. Pure Appl. Math. (to appear)
Birbrair, L., Fernandes, A., Neumann, W.: Bi-Lipschitz geometry of complex surface singularities. (preprint arXiv:0804.0194)
Brasselet, J.P., Goresky, M., MacPherson, R.: Simplicial differential forms with poles. Am. J. Math. 113, 1019–1052 (1991)
Neumann, W., Jankins, M.: Lectures on Seifert manifolds. Brandeis Lecture Notes, vol. 2. Brandeis University, Waltham (1983)
Scott, P.: The geometries of 3-manifolds. Bull. Lond. Math. Soc. 15, 401–487 (1983)
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L. Birbrair was supported under CNPq grant no. 300985/93-2. A. Fernandes was supported under CNPq grant no. 300393/2005-9. W. D. Neumann was supported under NSA grant H98230-06-1-011 and NSF grant no. DMS-0206464.
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Birbrair, L., Fernandes, A. & Neumann, W.D. Bi-Lipschitz geometry of weighted homogeneous surface singularities. Math. Ann. 342, 139–144 (2008). https://doi.org/10.1007/s00208-008-0225-4
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DOI: https://doi.org/10.1007/s00208-008-0225-4