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Characteristic classes and existence of singular maps


Authors: Boldizsár Kalmár and Tamás Terpai
Journal: Trans. Amer. Math. Soc. 364 (2012), 3751-3779
MSC (2010): Primary 57R45; Secondary 57R75, 57R25, 57R20
DOI: https://doi.org/10.1090/S0002-9947-2012-05544-9
Published electronically: February 17, 2012
MathSciNet review: 2901233
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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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Additional Information

Boldizsár Kalmár
Affiliation: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13-15, 1053 Budapest, Hungary
Email: kalmar.boldizsar@renyi.mta.hu

Tamás Terpai
Affiliation: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13-15, 1053 Budapest, Hungary
Email: terpai@math.elte.hu

DOI: https://doi.org/10.1090/S0002-9947-2012-05544-9
Keywords: Singularity, Morin map, fold map, blowup, Morse-Bott map, cobordism, Dold relations, geometric dimension.
Received by editor(s): June 7, 2010
Received by editor(s) in revised form: December 15, 2010, and January 7, 2011
Published electronically: February 17, 2012
Additional Notes: The first author was partially supported by the Magyary Zoltán Postdoctoral Fellowship and OTKA grant NK81203.
The second author was supported by OTKA grant NK81203.
Article copyright: © Copyright 2012 American Mathematical Society

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