The Lefschetz number of self-maps of Lie groups
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- by Hai Bao Duan PDF
- Proc. Amer. Math. Soc. 104 (1988), 1284-1286 Request permission
Abstract:
In this note we present a simple approach to the Lefschetz number for the self-maps of Lie groups. As an application it is proved that for any map $f:G \to G$ of a compact connected Lie group $G$, there is a solution to ${(f(x))^k} = x$ for some $k \leq \leftthreetimes + 1$, where $\leftthreetimes$ is the rank of the group $G$.References
- Sigurdur Helgason, Differential geometry, Lie groups, and symmetric spaces, Pure and Applied Mathematics, vol. 80, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 514561
- Morris W. Hirsch, Differential topology, Graduate Texts in Mathematics, vol. 33, Springer-Verlag, New York, 1994. Corrected reprint of the 1976 original. MR 1336822
- George W. Whitehead, Elements of homotopy theory, Graduate Texts in Mathematics, vol. 61, Springer-Verlag, New York-Berlin, 1978. MR 516508, DOI 10.1007/978-1-4612-6318-0
- Robert F. Brown, The Lefschetz fixed point theorem, Scott, Foresman & Co., Glenview, Ill.-London, 1971. MR 0283793
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 1284-1286
- MSC: Primary 55M20; Secondary 57T10
- DOI: https://doi.org/10.1090/S0002-9939-1988-0935107-8
- MathSciNet review: 935107