Periodic homotopy and conjugacy idempotents
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- by Jaka Smrekar PDF
- Proc. Amer. Math. Soc. 135 (2007), 4045-4055 Request permission
Abstract:
A self-map $f$ on the CW complex $Z$ is a periodic homotopy idempotent if for some $r\geqslant 0$ and $p>0$ the iterates $f^r$ and $f^{r+p}$ are homotopic. Geoghegan and Nicas defined the rotation index $RI(f)$ of such a map. They proved that for $r=p=1$, the homotopy idempotent $f$ splits if and only if $RI(f)=1$, while for $r=0$, the index $RI(f)$ divides $p^2$. We extend this to arbitrary $p$ and $r$, and generalize various results related to the splitting of homotopy idempotents on CW complexes and conjugacy idempotents on groups.References
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Additional Information
- Jaka Smrekar
- Affiliation: Fakulteta za matematiko in fiziko, Jadranska ulica 19, SI-1111 Ljubljana, Slovenia
- Email: jaka.smrekar@fmf.uni-lj.si
- Received by editor(s): April 26, 2006
- Received by editor(s) in revised form: September 6, 2006
- Published electronically: August 15, 2007
- Additional Notes: The author was supported in part by the MŠZŠ of the Republic of Slovenia research program No. P1-0292-0101-04 and research project No. J1-6128-0101-04, and in part by the DURSI of the Generalitat de Catalunya grant 2004-CRED-00048.
- Communicated by: Alexander N. Dranishnikov
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 4045-4055
- MSC (2000): Primary 55P99; Secondary 20F38, 57M07, 57M10
- DOI: https://doi.org/10.1090/S0002-9939-07-08900-9
- MathSciNet review: 2341957