Topological Classification and Finite Determinacy of knotted maps
Abstract
We show that the knot type of the link of a real analytic map germ with isolated singularity $f\colon(\mathbb{R}^2,0)\to(\mathbb{R}^4,0)$ is a complete invariant for $C^0$-$\mathscr A$-equivalence. Moreover, we also prove that isolated instability implies $C^0$-finite determinacy, giving an explicit estimate for its degree. For the general case of real analytic map germs, $f\colon (\mathbb{R}^n,0) \rightarrow (\mathbb{R}^p,0)$ ($n \leq p$), we use the Lojasiewicz exponent associated to the Mond's double point ideal $I^2(f)$ to obtain some criteria of Lipschitz and analytic regularity.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2018
- DOI:
- 10.48550/arXiv.1811.01113
- arXiv:
- arXiv:1811.01113
- Bibcode:
- 2018arXiv181101113J
- Keywords:
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- Mathematics - Algebraic Geometry
- E-Print:
- 16 pages