Members & Guests

Prof. Dr. Sebastian Goette

Project leader


Albert-Ludwigs-Universität Freiburg im Breisgau

E-mail: sebastian.goette(at)math.uni-freiburg.de
Telephone: +49 761 203 5571
Homepage: http://home.mathematik.uni-freiburg.de/g…

Project

4Secondary invariants for foliations

Publications within SPP2026

In a previous work, a six-parameter family of highly connected 7-manifolds which admit an $\mathrm{SO}(3)$-invariant metric of non-negative sectional curvature was constructed. Each member of this family is the total space of a Seifert fibration with generic fibre $\mathbb S^3$ and, in particular, has the cohomology of an $\mathbb S^3$-bundle over $\mathbb S^4$. In the present article, the linking form of these manifolds is computed and used to demonstrate that the family contains infinitely many manifolds which are not even homotopy equivalent to an $\mathbb S^3$-bundle over $\mathbb S^4$, the first time that any such spaces have been shown to admit non-negative sectional curvature.

 

 

 

Related project(s):
4Secondary invariants for foliations11Topological and equivariant rigidity in the presence of lower curvature bounds

In this short note we observe the existence of free, isometric actions of finite cyclic groups on a family of 2-connected 7-manifolds with non-negative sectional curvature. This yields many new examples including fake, and possible exotic, lens spaces.

 

 

 

Related project(s):
4Secondary invariants for foliations11Topological and equivariant rigidity in the presence of lower curvature bounds

In this article, a six-parameter family of highly connected 7-manifolds which admit an SO(3)-invariant metric of non-negative sectional curvature is constructed and the Eells-Kuiper invariant of each is computed. In particular, it follows that all exotic spheres in dimension 7 admit an SO(3)-invariant metric of non-negative curvature.

 

Related project(s):
4Secondary invariants for foliations11Topological and equivariant rigidity in the presence of lower curvature bounds

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