The Chess conjecture

Details The Chess conjecture The Chess conjecture

2003-01-31

arxiv.org/abs/math/0301371v2

Algebr. Geom. Topol. 3 (2003) 777-789

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-26.abs.html

Scientific paper

We prove that the homotopy class of a Morin mapping f: P^p --> Q^q with p-q odd contains a cusp mapping. This affirmatively solves a strengthened version of the Chess conjecture [DS Chess, A note on the classes [S_1^k(f)], Proc. Symp. Pure Math., 40 (1983) 221-224] and [VI Arnol'd, VA Vasil'ev, VV Goryunov, OV Lyashenko, Dynamical systems VI. Singularities, local and global theory, Encyclopedia of Mathematical Sciences - Vol. 6 (Springer, Berlin, 1993)]. Also, in view of the Saeki-Sakuma theorem [O Saeki, K Sakuma, Maps with only Morin singularities and the Hopf invariant one problem, Math. Proc. Camb. Phil. Soc. 124 (1998) 501-511] on the Hopf invariant one problem and Morin mappings, this implies that a manifold P^p with odd Euler characteristic does not admit Morin mappings into R^{2k+1} for p > 2k not equal to 1,3 or 7.

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