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Kato–Matsumoto-type results for disentanglements

Part of: Singularities Theory of singularities and catastrophe theory

Published online by Cambridge University Press:  20 February 2020

G. Peñafort Sanchis  and
M. Zach
G. Peñafort Sanchis
Affiliation:
Basque Center for Applied Mathematics, Mazarredo Zumarkalea, 14 48009Bilbo, Spain (gpenafort@bcamath.org)
M. Zach
Affiliation:
Institut für Mathematik, FB 08 - Physik, Mathematik und Informatik, Johannes Gutenberg-Universität, Staudingerweg 9, 4. OG, 55128Mainz, Germany (mazach@uni-mainz.de)
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Abstract

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We consider the possible disentanglements of holomorphic map germs f: (ℂn, 0) → (ℂN, 0), 0 < n < N, with nonisolated locus of instability Inst (f). The aim is to achieve lower bounds for their (homological) connectivity in terms of dim Inst (f). Our methods apply in the case of corank 1.

Keywords

Vanishing homologydisentanglementsconnectedness

MSC classification

Primary: 58K15: Topological properties of mappings
Secondary: 58K60: Deformation of singularities 32S30: Deformations of singularities; vanishing cycles
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 1 , February 2021 , pp. 1 - 27
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Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - SA
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Copyright
Copyright © Royal Society of Edinburgh 2020

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