Abstract
We determine the fundamental group of a closed n-manifold of positive sectional curvature on which a torus Tk (k large) acts effectively and isometrically. Our results are: (A) If k>(n − 3)/4 and n ≥ 17, then the fundamental group π1(M) is isomorphic to the fundamental group of a spherical 3-space form. (B) If k ≥ (n/6)+1 and n≠ 11, 15, 23, then any abelian subgroup of π1(M) is cyclic. Moreover, if the Tk-fixed point set is empty, then π1(M) is isomorphic to the fundamental group of a spherical 3-space form.
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Mathematics Subject Classification (2000). 53-XX
*Supported partially by NSF Grant DMS 0203164 and by a reach found from Beijing normal university.
**Supported partially by NSFC 10371008.
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Rong, X., Wang, Y. Fundamental Groups of Closed Manifolds with Positive Curvature and Torus Actions. Geom Dedicata 113, 165–184 (2005). https://doi.org/10.1007/s10711-005-3370-x
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DOI: https://doi.org/10.1007/s10711-005-3370-x