The relative coincidence Nielsen number

ArticleOriginal scientific text

Title

Authors ¹

Department of Mathematics, University of Agriculture, Nowoursynowska 166, 02-766 Warszawa, Poland

We define a relative coincidence Nielsen number

N_{r e l} (f, g)

for pairs of maps between manifolds, prove a Wecken type theorem for this invariant and give some formulae expressing

N_{r e l} (f, g)

by the ordinary Nielsen numbers.

[B] R. Brown, The Lefschetz Fixed Point Theorem, Scott, Foresman and Co., New York, 1971.
[BS] R. Brown and H. Schirmer, Nielsen coincidence theory and coincidence-producing maps for manifolds with boundary, Topology Appl. 46 (1992), 65-79.
[DJ] R. Dobreńko and J. Jezierski, The coincidence Nielsen theory on non-orientable manifolds, Rocky Mountain J. Math. 23 (1993), 67-85.
[Je1] J. Jezierski, The Nielsen number product formula for coincidences, Fund. Math. 134 (1989), 183-212.
[Je2] J. Jezierski, The semi-index product formula, ibid. 140 (1992), 99-120.
[Je3] J. Jezierski, The coincidence Nielsen number for maps into real projective spaces, ibid. 140 (1992), 121-136.
[Je4] J. Jezierski, The coincidence Nielsen theory on topological manifolds, ibid. 143 (1993), 167-178.
[Je5] J. Jezierski, The Lefschetz coincidence number on non-orientable manifolds, submitted.
[Ji] B. J. Jiang, Lectures on the Nielsen Fixed Point Theory, Contemp. Math. 14, Amer. Math. Soc., Providence, 1983.
[S1] H. Schirmer, Mindestzahlen von Koinzidenzpunkten, J. Reine Angew. Math. 194 (1955), 21-39.
[S2] H. Schirmer, A relative Nielsen number, Pacific J. Math. 122 (1986), 459-473.
[Y] C. Y. You, Fixed points of a fibre map, ibid. 100 (1982), 217-241.

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