The multiplicity mod 2 is not a bi-lipschitz invariant
A. Fernandes, Z. Jelonek, J.E. Sampaio
TL;DR
This paper demonstrates that the multiplicity mod 2 of real analytic sets is not preserved under subanalytic bi-Lipschitz homeomorphisms, challenging assumptions about invariants in real analytic geometry.
Contribution
It provides a counterexample showing that multiplicity mod 2 is not a bi-Lipschitz invariant for real analytic sets.
Findings
Multiplicity mod 2 is not preserved under bi-Lipschitz homeomorphisms.
Counterexamples to invariance of multiplicity mod 2.
Challenges previous beliefs about invariants in real analytic geometry.
Abstract
We show that subanalytic bi-Lipschitz homeomorphisms in general does not preserve the multiplicities of real analytic sets.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Differential Equations and Dynamical Systems · Mathematical Dynamics and Fractals