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Giacobbe, Andrea (2007) Fractional monodromy: parallel transport of homology cycles. [Journal papers (printed)] (In pubblicazione)

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Abstract (english)

A 2n-dimensional completely integrable system gives rise to a singular fibration whose generic fiber is the n-torus. In the classical setting, it is possible define a transformation of the fundamental group of the torus onto itself by parallel transporting along a path. This transformation is called monodromy transformation. Some systems give rise to a non-classical setting, in which the path is forced to cross a codimension 1 submanifold (a wall) of singular fibers, nonetheless a non-classical parallel transport can be defined on a subgroup of the fundamental group. This gives rise to what is known as monodromy with fractional coefficient.

In this article, we give a precise meaning to the non-classical parallel transport. In particular we show that it is a homologic process and not a homotopic one. We justify this statement by describing the type of singular fibers that generate a wall that can be crossed, by describing the parallel transport in a semi-local neighbourhood of the wall of singularities, and by producing a family of 4-dimensional examples.

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EPrint type:Journal papers (printed)
Anno di Pubblicazione:2007
Key Words:Completely integrable systems, Singular fibers, Monodromy transformation.
Settori scientifico-disciplinari MIUR:Area 01 - Scienze matematiche e informatiche > MAT/07 Fisica matematica
Struttura di riferimento:Dipartimenti > Dipartimento di Matematica
Codice ID:72
Depositato il:04 Apr 2007
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