Topological equivalence of finitely determined real analytic plane-to-plane map germs

Olav Skutlaberg

Abstract


Generic smooth map germs $({\mathsf R}^2,0)\to ({\mathsf R}^2,0)$ are topologically equivalent to cones of mappings $S^1\to S^1$. We carry out a complete topological classification of smooth stable mappings of the circle and show how this classification leads, via the result mentioned above, to a topological classification of finitely determined real analytic map germs $({\mathsf R}^2,0)\to ({\mathsf R}^2,0)$.

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DOI: http://dx.doi.org/10.7146/math.scand.a-15183

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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