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Zapiski Nauchnykh Seminarov LOMI, 1982, Volume 122, Pages 135–136
(Mi znsl4092)
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This article is cited in 1 scientific paper (total in 1 paper)
Nielsen numbers and fixed points of self-mappings of wedges of circles
V. G. Turaev
Abstract:
It is well known that if $f$ is a self-mapping of a compact connected polyhedron then $f$ has at least $N(f)$ fixed points where $N(f)$ denotes the Hielsen number of $f$. The present paper shows that for some self-mappings of $S^1\vee S^1$ tnis estimate is far from being precise. Namely, the following theorem is proved:
If $\alpha$ and $\beta$ are the canonical generators of $\pi_1(S^1\vee S^1)$ and if $f$ is a mapping $S^1\vee S^1\to S^1\vee S^1$ such that $f_\sharp(\alpha)=1$ and $f_\sharp(\beta)$ is conjugate to $(\alpha\beta\alpha^{-1}\beta^{-1})^n\alpha\beta\alpha^{-1}$ with $n\geqslant1$ then $N(f)=0$ and any mapping homotopic to $f$ has at least $2n-1$ fixed points.
Citation:
V. G. Turaev, “Nielsen numbers and fixed points of self-mappings of wedges of circles”, Investigations in topology. Part IV, Zap. Nauchn. Sem. LOMI, 122, "Nauka", Leningrad. Otdel., Leningrad, 1982, 135–136
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https://www.mathnet.ru/eng/znsl4092 https://www.mathnet.ru/eng/znsl/v122/p135
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Abstract page: | 135 | Full-text PDF : | 40 |
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