Equations in free groups and coincidence of mappings on surfaces |
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| Authors: | Daciberg L. Gonçalves Heiner Zieschang |
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| Affiliation: | Departamento de Matemática – IME-USP, Caixa Postal 66281 – Agência Cidade de S ao Paulo, 05315-970 S ao Paulo SP, Brasil (e-mail: dlgoncal@ime.usp.br), BR
Fakult?t für Mathematik, Ruhr – Universit?t Bochum, 44780 Bochum, Deutschland (e-mail: marlene.schwarz@ruhr-uni-bochum.de), DE
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| Abstract: | Let be a continuous map and a constant map between closed orientable surfaces of genus h,g, respectively. By definition the pair (f,c) has the Wecken property if f can be deformed into a map such that every coincidence classes of (f',c) is essential and consists of exactly one point. The main result is that (f,c) has the Wecken property if and only if where . Certain quadratic equations in free groups closely related to the coincidence problem are solved. Received January 26, 1999; in final form December 10, 1999 / Published online March 12, 2001 |
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| Keywords: | Mathematics Subject Classification (1991): 55M20 57M12 20F99 |
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