Topology of positively curved 8-dimensional manifolds with symmetry

Anand Dessai
2011 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 of
more » ... itive sectional curvature and symmetry rank ≥ 2. As an illustration, we apply our results to various families of 8-manifolds. MSC2000: 53C20, 57R19, 57S25.
doi:10.2140/pjm.2011.249.23 fatcat:ufknveude5aodjle656iy6wmgy