Abstract
The notion of a metric fibration was first introduced by Leinster. A metric fibration is said to be trivial if the total space is obtained by the cell_1 product of the base space and the fiber. A notable property of this is that its magnitude coincides with the product of the magnitudes of the base space and the fiber. It is known that for any odd-cycle graph, non-trivial fibrations do exist over the graph. On the other hand, any metric fibration over any even-cycle graph is trivial. In this talk, we focus on the existence of non-trivial metric fibrations. As a main result, we provide elementary proof that if the base space is a one-dimensional metric space, then only a trivial fibration exists.
Motivation
When are met fib trivial? Today: If the basis space is one-dimensional, then the fibration is trivial.
Wir definieren eine Metrische Faserung. Wir betrachten ein Beispiel, welches eine geometrische Realisierung von 6 Knoten sind, die durch einen zentralen Knoten verbunden sind.