Fernando Galaz-García

Positive sectional curvature on the exotic $8$-sphere and order-three homotopy $10$-spheres

We prove that the exotic smooth $8$-sphere and both oriented homotopy $10$-spheres representing elements of order three admit Riemannian metrics with strictly positive sectional curvature. The construction combines Speran\c{c}a's special $S^3$-$S^3$ bundle models with the compatible-disk construction of He, Liu and Yau...