Characteristic classes and existence of singular maps

Kalmár, Boldizsár; Terpai, Tamás

doi:10.1090/S0002-9947-2012-05544-9

Characteristic classes and existence of singular maps
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by Boldizsár Kalmár and Tamás Terpai

Trans. Amer. Math. Soc. 364 (2012), 3751-3779

DOI: https://doi.org/10.1090/S0002-9947-2012-05544-9

Published electronically: February 17, 2012

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Abstract:

The existence of a corank one map of negative codimension puts strong restrictions on the topology of the source manifold. It implies many vanishing theorems on characteristic classes and often even vanishing of the cobordism class of the source manifold. Most of our results lie deeper than just vanishing of Thom polynomials of the higher singularities. We blow up the singular map along the singular set and then perturb the arising nongeneric corank one map.

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