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The minimal number of roots of surface mappings and quadratic equations in free groups |
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| Authors: | Semeon Bogatyi Daciberg L Gonçalves Heiner Zieschang |
| Institution: | Mechanics and Mathematics Faculty, Moscow State University, Moscow 119899, Russia (e-mail: bogatyi@nw.math.msu.su), RU Departamento de Matemática - IME-USP, Caixa Postal 66281 - Agência Cidade de S ao Paulo, 05315-970 - Sao Paulo - SP - Brasil, (e-mail: dlgoncal@ime.usp.br), BR Fakult?t für Mathematik, Ruhr - Universit?t Bochum, 44780 Bochum - Germany, (e-mail: marlene.schwarz@ruhr-uni-bochum.de), DE |
| Abstract: | Let be a continuous mapping between orientable closed surfaces of genus h and g and let c denote the constant map with . Let be the minimal number of roots of f' among all maps f' homotopic to f, i.e. . We prove that where and denotes the Euler characteristic. In addition, certain quadratic equations in free groups closely related to the coincidence problem are solved. Received January 26, 1999; in final form November 8, 1999 / Published online February 5, 2001 |
| Keywords: | Mathematics Subject Classification (1991): 55M20 57M12 20F99 |
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