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We extend two known existence results to simply connected manifolds with positive sectional curvature: we show that there exist pairs of simply connected positively-curved manifolds that are tangentially homotopy equivalent but not homeomorphic, and we deduce that an open manifold may admit a pair of non-homeomorphic simply connected and positively-curved souls. Examples of such pairs are given by explicit pairs of Eschenburg spaces. To deduce the second statement from the first, we extend our earlier work on the stable converse soul question and show that it has a positive answer for a class of spaces that includes all Eschenburg spaces.

We calculate the additive and multiplicative structure of the ring $K\left( S\left( {{T}^{*}}\mathbb{R}{{P}^{2n+1}} \right) \right)$ using the eta invariant.

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Open manifolds with non-homeomorphic positively curved souls

THE GROMOV-LAWSON-ROSENBERG CONJECTURE FOR THE SEMI-DIHEDRAL GROUP OF ORDER 16

Multiplicative Structure of the Ring K(S(T*ℝP2n+1))

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3 results

Open manifolds with non-homeomorphic positively curved souls

THE GROMOV-LAWSON-ROSENBERG CONJECTURE FOR THE SEMI-DIHEDRAL GROUP OF ORDER 16

Multiplicative Structure of the Ring K(S(T*ℝP2n+1))