Celebratio Mathematica — Neumann — Complete Bibliography

Complete Bibliography

Works connected to José Antonio Seade Kuri

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W. D. Neumann and A. Pichon: “Lipschitz geometry does not determine embedded topological type,” pp. 183–195 in Singularities in geometry, topology, foliations and dynamics: A celebration of the 60th birthday of José Seade (Mérida, Mexico, 8–19 December 2014). Edited by J. L. Cisneros-Molina, D. Tráng Lê, M. Oka, and J. Snoussi. Trends in Mathematics. Birkhäuser (Cham, Switzerland), 2017. Dedicated to José Seade for a great occasion. Happy birthday, Pepe. MR 3706220 Zbl 1426.14003 ArXiv 1506.03841 incollection

We investigate the relationships between the Lipschitz outer geometry and the embedded topological type of a hypersurface germ in \( (\mathbb{C}^n,0) \). It is well known that the Lipschitz outer geometry of a complex plane curve germ determines and is determined by its embedded topological type. We prove that this does not remain true in higher dimensions. Namely, we give two normal hypersurface germs \( (X_1,0) \) and \( (X_2,0) \) in \( (\mathbb{C}^3,0) \) having the same outer Lipschitz geometry and different embedded topological types. Our pair consist of two superisolated singularities whose tangent cones form an Alexander–Zariski pair having only cusp-singularities. Our result is based on a description of the Lipschitz outer geometry of a superisolated singularity. We also prove that the Lipschitz inner geometry of a superisolated singularity is completely determined by its (non-embedded) topological type, or equivalently by the combinatorial type of its tangent cone.

Anne Pichon	Related
José Antonio Seade Kuri	Related

@incollection {key3706220m,
	AUTHOR = {Neumann, Walter D. and Pichon, Anne},
	TITLE = {Lipschitz geometry does not determine
		 embedded topological type},
	BOOKTITLE = {Singularities in geometry, topology,
		 foliations and dynamics: {A} celebration
		 of the 60th birthday of {J}os\'e {S}eade},
	EDITOR = {Cisneros-Molina, Jos\'e Luis and Tr\'ang
		 L\^e, D\~ung and Oka, Mutsuo and Snoussi,
		 Jawad},
	SERIES = {Trends in Mathematics},
	PUBLISHER = {Birkh\"auser},
	ADDRESS = {Cham, Switzerland},
	YEAR = {2017},
	PAGES = {183--195},
	DOI = {10.1007/978-3-319-39339-1_11},
	NOTE = {(M\'erida, Mexico, 8--19 December 2014).
		 Dedicated to Jos\'e Seade for a great
		 occasion. Happy birthday, Pepe!. ArXiv:1506.03841.
		 MR:3706220. Zbl:1426.14003.},
	ISSN = {2297-0215},
	ISBN = {9783319393384},
}