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Topology of positively curved 8-dimensional manifolds with symmetry
Pacific Journal of Mathematics
We show that a simply connected 8-dimensional manifold M of positive sectional curvature and symmetry rank ≥ 2 resembles a rank-one symmetric space in several ways. For example, the Euler characteristic of M is equal to the Euler characteristic of S 8 , ވ P 2 or ރ P 4 . If M is rationally elliptic, then M is rationally isomorphic to a rank-one symmetric space. For torsionfree manifolds, we derive a much stronger classification. We also study the bordism type of 8-dimensional manifolds ofdoi:10.2140/pjm.2011.249.23 fatcat:ufknveude5aodjle656iy6wmgy