@article {stupovski2020existence, title = {Existence of Riemannian metrics with positive biorthogonal curvature on simply connected 5-manifolds}, journal = {Archiv der Mathematik}, year = {2020}, pages = {1{\textendash}9}, publisher = {Springer}, abstract = {

Using the recent work of Bettiol, we show that a first-order conformal deformation of Wilking{\textquoteright}s metric of almost-positive sectional curvature on $S2\times S3$ yields a family of metrics with strictly positive average of sectional curvatures of any pair of 2-planes that are separated by a minimal distance in the 2-Grassmanian. A result of Smale allows us to conclude that every closed simply connected 5-manifold with torsion-free homology and trivial second Stiefel{\textendash}Whitney class admits a Riemannian metric with a strictly positive average of sectional curvatures of any pair of orthogonal 2-planes.

}, doi = {10.1007/s00013-020-01511-x}, url = {https://dx.doi.org/10.1007/s00013-020-01511-x}, author = {Boris Stupovski and Rafael Torres} } @article {2020, title = {Topology change and selection rules for high-dimensional spin(1,n)0-Lorentzian cobordisms}, journal = {Transactions of the american mathematical society}, volume = {373}, year = {2020}, pages = {1731-1747}, type = {Journal article}, chapter = {1731}, doi = {10.1090/tran/7939}, url = {http://hdl.handle.net/20.500.11767/108858}, author = {Gleb Smirnov and Rafael Torres} }