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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

1 vote
0 answers
305 views

Perfect groups of infinite order

Let $M$ be a closed, minimal, hypersurface in the sphere $S^{n-1}$, $n\geq 4$. Suppose $M$ has $H^1(M,\mathbb{Z})=0$. What can we say about the cardinality of the first fundamental group of $M$, $\pi_ …
Renan Assimos's user avatar
8 votes
0 answers
1k views

Homotopy groups of the Grassmannians

What are the homotopy groups of the oriented Grassmannian $Gr^{+}(p,q)$ (p-planes in $R^{p+q}$) $\pi_{r}(Gr^{+}(p,q))$, $r \le pq$? Do you know any references on the web about it?
Renan Assimos's user avatar