Monodromy representations of completed coverings

Aaltonen, Martina

doi:10.48550/arxiv.1406.6484

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2017

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“…For the general theory of these completions, see e.g. Fox [11], Berstein-Edmonds [2], Edmonds [8], or [1]. We call f ′ the regular part of f .…”

Section: 2mentioning

confidence: 99%

“…The monodromy triangle (1) of f : X → M is obtained as an extension of the monodromy triangle of its regular part f ′ : X ′ → M ′ . We refer to Berstein-Edmonds [2], or [1], for details.…”

Section: 2mentioning

confidence: 99%

“…Let f : M → N be a proper branched cover between n-manifolds. By a result of Berstein and Edmonds [2] (see also [1]), there exists a space X f and an action G f X f of the monodromy group G f of f by homeomorphisms for which the diagram…”

Section: Introductionmentioning

confidence: 99%

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Local monodromy of branched covers and dimension of the branch set

Aaltonen¹,

Pankka²

2017

Ann. Acad. Sci. Fenn. Math.

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Abstract. We show that, if the local dimension of the image of the branch set of a discrete and open mapping f : M → N between n-manifolds is less than (n − 2) at a point y of the image of the branch set f B f , then the local monodromy of f at y is perfect. In particular, for generalized branched covers between n-manifolds the dimension of f B f is exactly (n−2) at the points of abelian local monodromy. As an application, we show that a generalized branched covering f : M → N of local multiplicity at most three between n-manifolds is either a covering or f B f has local dimension (n − 2).

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“…For the general theory of these completions, see e.g. Fox [11], Berstein-Edmonds [2], Edmonds [8], or [1]. We call f ′ the regular part of f .…”

Section: 2mentioning

confidence: 99%

Section: 2mentioning

confidence: 99%