منابع مشابه
Surface branched covers and geometric 2-orbifolds
Let Σ̃ and Σ be closed, connected, and orientable surfaces, and let f : Σ̃ → Σ be a branched cover. For each branching point x ∈ Σ the set of local degrees of f at f−1(x) is a partition of the total degree d. The total length of the various partitions is determined by χ(Σ̃), χ(Σ), d and the number of branching points via the Riemann-Hurwitz formula. A very old problem asks whether a collection of ...
متن کاملConstructing Simplicial Branched Covers
Izmestiev and Joswig described how to obtain a simplicial covering space (the partial unfolding) of a given simplicial complex, thus obtaining a simplicial branched cover [Adv. Geom. 3(2):191-255, 2003]. We present a large class of branched covers which can be constructed via the partial unfolding. In particular, for d ≤ 4 every closed oriented PL d-manifold is the partial unfolding of some pol...
متن کاملCounting functions for branched covers of elliptic curves and quasi-modular forms
of the branched covers of an elliptic curve. Here, N (m) g,d is the (weighted) number of isomorphism classes of branched covers, with genus g(> 1), degree d, and ramification index (m,m, . . . ,m), of an elliptic curve. Such a cover is called an m-simple cover. Our aim is to prove that the formal power series F (m) g converges to a function belonging to the graded ring of quasi-modular forms wi...
متن کاملKnot Floer homology in cyclic branched covers
In this paper, we introduce a sequence of invariants of a knot K in S3 : the knot Floer homology groups ĤFK(Σm(K); K̃, i) of the preimage of K in the m–fold cyclic branched cover over K . We exhibit ĤFK(Σm(K); K̃, i) as the categorification of a well-defined multiple of the Turaev torsion of Σm(K)− K̃ in the case where Σm(K) is a rational homology sphere. In addition, when K is a two-bridge knot, ...
متن کاملOn Branched Covers in Topos Theory
We present some new findings concerning branched covers in topos theory. Our discussion involves a particular subtopos of a given topos that can be described as the smallest subtopos closed under small coproducts in the including topos. Our main result is a description of the covers of this subtopos as a category of fractions of branched covers, in the sense of Fox [10], of the including topos....
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ژورنال
عنوان ژورنال: Studia Scientiarum Mathematicarum Hungarica
سال: 2019
ISSN: 0081-6906,1588-2896
DOI: 10.1556/012.2019.56.3.1431