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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747

The Chess conjecture

Rustam Sadykov

Algebraic & Geometric Topology 3 (2003) 777–789

DOI: 10.2140/agt.2003.3.777

arXiv: math.GT/0301371

Abstract

We prove that the homotopy class of a Morin mapping f:Pp→Qq 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 [S1k(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 Pp with odd Euler characteristic does not admit Morin mappings into R2k+1 for p≥ 2k+1≠1,3,7.

Keywords

singularities, cusps, fold mappings, jets

Mathematical Subject Classification

Primary: 57R45

Secondary: 58A20, 58K30

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Publication

Received: 18 February 2003
Revised: 23 July 2003
Accepted: 19 August 2003
Published: 24 August 2003

Authors
Rustam Sadykov
University of Florida
Department of Mathematics
358 Little Hall, 118105
Gainesville, FL 32611-8105
USA