Multiplicity and degree as bi‐Lipschitz invariants for complex sets. Issue 4 (29th August 2018)

• Record Type: Journal Article
• Authors: Fernández de Bobadilla, Javier; Fernandes, Alexandre; Sampaio, J. Edson
• Is Part Of: Journal of topology. Volume 11:Issue 4(2018)
• Page Start: 958
• Page End: 966
• Publication Date: 2018-08-29
• Subjects: 14B05 -- 32S50 (primary); Topology -- Periodicals; 514.05
• DOI: 10.1112/topo.12080
• Languages: English
• ISSNs: 1753-8416

Abstract

Abstract: We study invariance of multiplicity of complex analytic germs and degree of complex affine sets under outer bi‐Lipschitz transformations (outer bi‐Lipschitz homeomorphims of germs in the first case and outer bi‐Lipschitz homeomorphims at infinity in the second case). We prove that invariance of multiplicity in the local case is equivalent to invariance of degree in the global case. We prove invariance for curves and surfaces. In the way we prove invariance of the tangent cone and relative multiplicities at infinity under outer bi‐Lipschitz homeomorphims at infinity, and that the abstract topology of a homogeneous surface germ determines its multiplicity.