|
|
Петербургский геометрический семинар им. А. Д. Александрова
7 марта 2022 г. 17:00–19:00, г. Санкт-Петербург, Дистанционно в ZOOM.
|
 |
|
 |
|
|
|
[On collapse of tori under lower sectional curvature bounds]
, Sergio Zamora Barrera |
| Количество просмотров: |
| Эта страница: | 80 |
|
Аннотация:
Let $X_i$ be a sequence of closed $n$-dimensional Riemannian manifolds of sectional curvature bounded below,
and diameter bounded above. It is well known that one can always find a subsequence that converges in the
Gromov–Hausdorff sense to a compact geodesic space $X$ of dimension $\leq n$.
When $X$ has dimension $n$, Perelman showed that it is homeomorphic to $X_i$ for $i$ large enough.
In other words, the topology stabilizes. On the other hand, the problem of understanding the geometry and topology
of $X$ when its dimension is strictly less than $n$ is hard to attack and not much is known when $X$ is highly
singular.
We will discuss the particular case when the spaces are homeomorphic to the $n$-dimensional torus,
where I have shown that the fundamental group can be recovered by the fibration part, generalizing a recent
result by Mikhail Katz and showing that in this case, if $X$ is a $C^1$-Riemannian manifold with boundary,
then its first Betti is at least its dimension.
Язык доклада: Английский
|
|
Обратная связь: