Real Algebraic and Analytic Geometry
Submission: 2006, August 11.
We produce examples of complex algebraic surfaces with isolated singularities such that these singularities are not metrically conic, i.e. the germs of the surfaces near singular points are not bi-Lipschitz equivalent, with respect to inner metric, to cones. The technique used to prove the nonexistence of the metric conic structure is related to a development of Metric Homology.
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