Riemannian Topology Seminar 2013
F-Structures in Geometry and Topology
November 28 - 29, 2013
Organizers:
Prof. Dr. A. Dessai (Fribourg)
Prof. Dr. W. Tuschmann (Karlsruhe)
Topic
F-Structures, having been introduced by Gromov in the late seventies, play an important role in the structure theory of Riemannian manifolds which collapse under certain curvature bounds. Since, on the other hand, they can also just be viewed as generalizations of group actions, one may approach them as well from a purely differential topological point of view in the realm of studying symmetry structures and dynamical systems on manifolds.
The seminar aims at presenting and highlighting their main respective features as well as at identifying new directions of further research on F-structures in geometry and topology. Based on the discussions among and interests of the participants, more advanced and specialized related topics like, e.g., F-structures and collapsing in the work of Naber-Tian, fF-structures, or F-structures, foliations and cobordism, will be treated in a sequel seminar.
Program
All talks on thursday will take place in the 'Seminarraum K 2' at Kronenstraße 32, across the square the mathematics building is located at.
| Thursday, 28. November 2013 | |
|---|---|
| Seminarraum K 2 | |
15:30 - 16:00 |
Introduction |
16:00 - 17:00 |
F-Structures: definitions and examples I |
Coffee break |
|
17:30 - 18:30 |
F-Structures: definitions and examples II |
Dinner |
|
On the second day the talks will be held in a different room, 'Seminarraum Z 1' in the 'Zähringerhaus' at Fritz-Erler-Str. 1. Its entrance is up the winding-stairs, to the left of the mathematical library.
| Friday, 29. November 2013 | |
|---|---|
| Seminarraum Z 1 | |
10:00 - 11:00 |
Almost flat manifolds |
Coffee break |
|
11:30 - 12:30 |
F-Structures and collapsing |
Lunch break |
|
14:30 - 15:30 |
F-Structures and topology |
Coffee break |
|
16:00 - 17:00 |
F-Structures, entropy and the Bott conjecture |
Literature
Cheeger, Jeff; Gromov, Mikhael. Collapsing Riemannian manifolds while keeping their curvature bounded. I. J. Differential Geom. 23 (1986), no. 3, 309-346.
Cheeger, Jeff; Gromov, Mikhael. Collapsing Riemannian manifolds while keeping their curvature bounded. II. J. Differential Geom. 32 (1990), no. 1, 269-298.
Cheeger, Jeff; Fukaya, Kenji; Gromov, Mikhael. Nilpotent structures and invariant metrics on
collapsed manifolds J. Amer. Math. Soc. 5 (1992), no. 2, 327–372.
Fukaya, Kenji. Collapsing Riemannian manifolds to ones of lower dimensions J. Differential
Geom. 25 (1987), no. 1, 139–156.
Fukaya, Kenji. A boundary of the set of the Riemannian manifolds with bounded curvatures and
diameters J. Differential Geom. 28 (1988), no. 1, 1–21.
Fukaya, Kenji. Collapsing Riemannian manifolds to ones with lower dimension. II J. Math. Soc.
Japan 41 (1989), no. 2, 333–356.
Fukaya, Kenji. Hausdorff convergence of Riemannian manifolds and its applications. In: Recent
topics in differential and analytic geometry, ed. by T.Ochiai. Advanced Studies in Pure Math.
18-1. Kinokuniya, Academic Press, Tokyo Boston 1990.
Ghanaat, Patrick. Geometric construction of holonomy coverings for almost flat manifolds. J. Differential Geom. 34 (1991), no. 2, 571-580.
Gromov, Mikhail. Almost flat manifolds. J. Differential Geom. 13 (1978), no. 2, 231-241.
Kapovitch, Vitali; Petrunin, Anton; Tuschmann, Wilderich. Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces. Ann. Math. (2) 171 (2010), no. 1, 343-373.
Paternain, Gabriel P.; Petean, Jimmy. Minimal entropy and collapsing with curvature bounded from below. Invent. Math. 151 (2003), no. 2, 415-450.
Paternain, Gabriel P.; Petean, Jimmy. Zero entropy and bounded topology. Comment. Math. Helv. 81 (2006), no. 2, 287-304.
Ruh, Ernst. Almost flat manifolds. J. Differential Geom. 17 (1982), no. 1, 1-14.