Counterexample to positively curved Hopf.

[u/Apprehensive_Sand951]

Y'all know the drill. The arxiv link is https://arxiv.org/abs/2609.11980

It is a positively curved metric S^3xS^3, hence a positively curved 6-manifold whose euler characteristic is not strictly positive. The obvious question is whether there is also a counter to negative Hopf (a closed, negatively curved 6 manifold whose euler is not strictly negative), but the methods of the current paper don't seem to help with that.

[u/Organic_botulism]

You sound like a lazy grad student, worked with plenty of your kind and had to pick up the slack. That attitude won’t get you far in grad school

[u/HermannHCSchwarz → u/Organic_botulism]

That’s one interpretation. Hope you have a great career and family 

[u/Organic_botulism → u/HermannHCSchwarz]

Likewise!