Positive Curvature, Symmetries, and Matroids
Positive Curvature, Symmetries, and Matroids
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Michael Wiemeler, M眉nster
Online Talk听
Zoom link:听
Passcode: 114700
A 1930s conjecture of Hopf states that the Euler characteristic of听 a positively curved even-dimensional manifold is positive. In joint work with Lee Kennard and Burkhard Wilking we showed this conjecture for simply connected manifolds $M$ with isometric, effective $T^5$-action. If there is an isometric, effective $T^7$-action on $M$ and the odd-degree rational cohomology of $M$ vanishes, we can also compute the rational cohomology ring of $M$.
In this talk I will discuss a similar result where the above cohomological condition is replaced by a "more geometric" one. Its proof is an application of matroid theory. The results presented in this talk are joint work with Lee Kennard and Burkhard Wilking.