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A SHORT NOTE ON THE THOM–BOARDMAN SYMBOLS OF DIFFERENTIABLE MAPS

Part of: Surfaces and higher-dimensional varieties Theory of singularities and catastrophe theory

Published online by Cambridge University Press:  04 March 2012

YULAN WANG ,
JIAYUAN LIN  and
MAORONG GE
YULAN WANG
Affiliation:
Anhui Economic Management Institute, Hefei, Anhui 230059, China Department of Mathematics, SUNY Canton, 34 Cornell Drive, Canton, NY 13617, USA
JIAYUAN LIN*
Affiliation:
Department of Mathematics, SUNY Canton, 34 Cornell Drive, Canton, NY 13617, USA (email: [email protected])
MAORONG GE
Affiliation:
School of Mathematics and Computational Science, Anhui University, Hefei, Anhui 230039, China
*
✉For correspondence; e-mail: [email protected]
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Abstract

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It is well known that Thom–Boardman symbols are realized by nonincreasing sequences of nonnegative integers. A natural question is whether the converse is also true. In this paper we answer this question affirmatively, that is, for any nonincreasing sequence of nonnegative integers, there is at least one map-germ with the prescribed sequence as its Thom–Boardman symbol.

Keywords

Thom–Boardman symbolJacobian extensioncritical extension

MSC classification

Secondary: 58K40: Classification; finite determinacy of map germs 58K20: Algebraic and analytic properties of mappings 14J17: Singularities
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 92 , Issue 3 , June 2012 , pp. 385 - 390
Copyright
Copyright © 2013 Australian Mathematical Publishing Association Inc.

References

[1]Adams, M., McCrory, C., Shifrin, T. and Varley, R., ‘Invariants of Gauss maps of theta divisors’, in: Differential Geometry: Geometry in Mathematical Physics and Related Topics, Proceedings of Symposia in Pure Mathematics, 54 (American Mathematical Society, Providence, RI, 1993), pp. 1–8.Google Scholar
[2]Arnol’d, V. I., Guseĭn-Zade, S. M. and Varchenko, A. N., Singularities of Differentiable Maps, Vol. 1 (Birkhäuser, Boston, 1985).CrossRefGoogle Scholar
[3]Lin, J. and Wethington, J., ‘On the Thom–Boardman symbols for polynomial multiplication maps’, Asian J. Math. (3) 16 (2012), 367–386.CrossRefGoogle Scholar