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The least number of coincidence points on surfaces

Part of: Differential topology Classical Topics in Algebraic Topology

Published online by Cambridge University Press:  09 April 2009

Jerzy Jezierski
Jerzy Jezierski
Affiliation:
Department of Mathematics, University of Agriculture, Nowoursynowska 166, 02 766 Warsaw, Poland
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Abstract

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Bo Ju Jiang introduced an invariant lying in the braid group which is the best lower bound of the number of fixed points in a homotopy class of a given pair of self maps of a surface. Here we modify this construction to get a lower bound of the number of coincidence points of a pair of maps between two closed surfaces.

MSC classification

Secondary: 55M20: Fixed points and coincidences 57R99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 58 , Issue 1 , February 1995 , pp. 27 - 38
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Brooks, R., ‘On removing coincidences of two maps when only one, rather than both, of them may be deformed by a homotopy’, Pacific J. Math. 40 (1972), 45–52.CrossRefGoogle Scholar
[2]Brown, R. F., The Lefschetz fixed point theorem (Scott, Foresman and Co., Glenview, 1971).Google Scholar
[3]Dobreńko, R. and Jezierski, J., ‘The coincidence Nielsen number on non-orientable manifolds’, Rocky Mountain J. Math. 23 (1993), 67–85.CrossRefGoogle Scholar
[4]Jezierski, J., ‘The Nielsen number product formula for coincidences’, Fund. Math. 134 (1989), 183–212.CrossRefGoogle Scholar
[5]Jezierski, J., ‘The coincidence Nielsen number for maps into real projective spaces’, Fund. Math. 140 (1992), 121–136.CrossRefGoogle Scholar
[6]Jezierski, J., ‘The semi-index product formula’, Fund. Math. 140 (1992), 99–120.CrossRefGoogle Scholar
[7]Jiang, B. J., ‘On the Nielsen number of fixed points’, Amer. J. Math. 102 (1980), 749–763.Google Scholar
[8]Jiang, B. J., ‘Lectures on the Nielsen fixed point theory’, Contemp. Math. 14 (Amer. Math. Soc., Providence, 1983).Google Scholar
[9]Jiang, B. J., ‘Fixed points and braids’, Invent. Math. 75 (1985), 69–74.CrossRefGoogle Scholar
[10]Jiang, B. J., ‘Surface maps and braid equations, I’, Lecture Notes in Math. 1369 (Springer, New York, 1989) pp. 125–141.Google Scholar
[11]Olum, P., ‘Obstructions to extensions and homotopies’, Ann. of Math. (2) 52 (1950), 1–50.CrossRefGoogle Scholar
[12]Shi, G. H., ‘On the least number of fixed points and Nielsen numbers’, Acta Math. Sinica 16 (1966), 223–232Google Scholar
(Chinese Math. Acta 8 (1966), 234–243).Google Scholar