منابع مشابه
Branched Covers of Hyperbolic Manifolds and Harmonic Maps
Let f : M → N be a homotopy equivalence between closed negatively curved manifolds. The fundamental existence results of Eells and Sampson [5] and uniqueness of Hartmann [15] and Al’ber [1] grant the existence of a unique harmonic map h homotopic to f . Based on the enormous success of the harmonic map technique Lawson and Yau conjectured that the harmonic map h should be a diffeomorphism. This...
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 کاملEmbedding 3-manifolds in 4-space and link concordance via double branched covers
The double branched cover is a construction which provides a link between problems in knot theory and other questions in low-dimensional topology. Given a knot in a 3-manifold, the double branched cover gives a natural way of associating a 3-manifold to the knot. Similarly, the double branched cover of a properly embedded surface in a 4-manifold is a 4-manifold whose boundary is the double bran...
متن کاملFinite Type Invariants of Cyclic Branched Covers
Given a knot in an integer homology sphere, one can construct a family of closed 3-manifolds (parametrized by the positive integers), namely the cyclic branched coverings of the knot. In this paper we give a formula for the the Casson-Walker invariants of these 3-manifolds in terms of residues of a rational function (which measures the 2-loop part of the Kontsevich integral of a knot) and the s...
متن کاملOn the nonexistence of certain branched covers
Starting with the classical result of Alexander [1], asserting that every closed, orientable PL–manifold of dimension n admits a branched cover onto the n–dimensional sphere S , a series of authors such as Berstein and Edmonds [3], Edmonds [11], Hilden [15], Hirsch [16], Iori and Piergallini [18], Montesinos [19] and Piergallini [20] have proved the existence of branched covers satisfying certa...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2018
ISSN: 0001-8708
DOI: 10.1016/j.aim.2018.04.016