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October 2020 Topological Classification and Finite Determinacy of Knotted Maps
Juan J. Nuño-Ballesteros, Rodrigo Mendes
Michigan Math. J. 69(4): 831-848 (October 2020). DOI: 10.1307/mmj/1585792886

Abstract

We show that the knot type of the link of a real analytic map germ with isolated singularity f : ( R 2 , 0 ) ( R 4 , 0 ) is a complete invariant for C 0 - A -equivalence. Moreover, we also prove that isolated singularity implies finite C 0 -determinacy, giving an explicit estimate for its degree. For the general case of real analytic map germs, f : ( R n , 0 ) ( R p , 0 ) ( n p ), we use the Lojasiewicz exponent associated with Mond’s double point ideal I 2 ( f ) to obtain some criteria of Lipschitz and analytic regularity.

Citation

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Juan J. Nuño-Ballesteros. Rodrigo Mendes. "Topological Classification and Finite Determinacy of Knotted Maps." Michigan Math. J. 69 (4) 831 - 848, October 2020. https://doi.org/10.1307/mmj/1585792886

Information

Received: 16 November 2018; Revised: 31 May 2019; Published: October 2020
First available in Project Euclid: 2 April 2020

MathSciNet: MR4168788
Digital Object Identifier: 10.1307/mmj/1585792886

Subjects:
Primary: 14P25, 57M25, 58K15

Rights: Copyright © 2020 The University of Michigan

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Vol.69 • No. 4 • October 2020
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