Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

DMV Tagung 2011 - Köln, 19. - 22. September
Christian Becker
Universität Potsdam
Fiber integration for Cheeger-Simons differential characters
The group of differential characters fits into several short exact sequences relating it to smooth singular
cohomology and differential forms. On a smooth fiber bundle with compact oriented fibers there are
natural fiber integration maps for differential forms and smooth singular cohomology. We prove existence
and uniqueness of the fiber integration for differential characters, both for fiber bundles with closed fibers
and for fibers with boundary. The fiber integration commutes with the exact sequences. As an application,
we construct the transgression to loop spaces and more general mapping spaces.
Ruth Kellerhals
University of Fribourg
Small hyperbolic orbifolds, scissors congruence and arithmetic
We give a survey about hyperbolic orbifolds realising minimal volume and discuss the problem and results
about how to detect and characterise them. In the focus are the combinatorial and arithmetical properties
in the 5-dimensional case. We report about ongoing work together with Vincent Emery.
Rolfdieter Frank
Universität Koblenz-Landau
Eine einfache Formel für das Volumen beliebiger Hyperebenenschnitte des n-dimensionalen
Würfels
Im Vortrag geht es um den folgenden Satz, den ich gemeinsam mit Harald Riede bewiesen habe: Ist
Cn = [−1,1] n ein n-dimensionaler Würfel, a = (a1,...,an) ∈ (R \ {0}) n , b ∈ R und
H = {x ∈ R n |a · x = b}, so gilt
|a|
Vol(Cn ∩ H) =
2(n − 1)! ·
n
∏
k=1
a −1
k · ∑
w∈{1,−1} n
(a · w + b) n−1 · sgn(a · w + b) ·
n
∏ wk .
k=1
Zum Beispiel ist C5 ∩ H mit H = {x ∈ R5 |x1 + x2 + x3 + x4 + x5 = 0} ein vierdimensionales
archimedisches Polytop. Unser Satz liefert Vol(C5 ∩ H) = 115
√
12 5 und dieses Ergebnis lässt sich geometrisch
bestätigen.
Bernd Hanke
Universität Augsburg
Positive scalar curvature, K-area and essentialness
We discuss several largeness properties of closed smooth manifolds and point out their geometric and
topological implications.
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