منابع مشابه
Linking Numbers in Rational Homology 3-spheres, Cyclic Branched Covers and Infinite Cyclic Covers
We study the linking numbers in a rational homology 3-sphere and in the infinite cyclic cover of the complement of a knot. They take values in Q and inQ(Z[t, t−1]) respectively, where Q(Z[t, t−1]) denotes the quotient field of Z[t, t−1]. It is known that the modulo-Z linking number in the rational homology 3-sphere is determined by the linking matrix of the framed link and that the modulo-Z[t, ...
متن کاملFinite Covers of the Infinite Cyclic Cover of a Knot
We show that the commutator subgroup G ′ of a classical knot group G need not have subgroups of every finite index, but it will if G ′ has a surjective homomorphism to the integers and we give an exact criterion for that to happen. We also give an example of a smoothly knotted S n in S n+2 for all n ≥ 2 whose infinite cyclic cover is not simply connected but has no proper finite covers.
متن کاملOn splitting infinite-fold covers
Let X be a set, κ be a cardinal number and let H be a family of subsets of X which covers each x ∈ X at least κ times. What assumptions can ensure that H can be decomposed into κ many disjoint subcovers? We examine this problem under various assumptions on the set X and on the cover H: among other situations, we consider covers of topological spaces by closed sets, interval covers of linearly o...
متن کاملMotivic Milnor Fibre of Cyclic L∞-algebras
We define motivic Milnor fibre of cyclic L∞-algebras of dimension three using the method of Denef and Loeser of motivic integration. It is proved by Nicaise and Sebag that the topological Euler characteristic of the motivic Milnor fiber is equal to the Euler characteristic of the étale cohomology of the analytic Milnor fiber. We prove that the value of Behrend function on the germ moduli space ...
متن کاملRank Gradient of Cyclic Covers
If M is an orientable hyperbolic 3-manifold with finite volume and φ : π1(M) Z, the family of covers corresponding to {φ−1(nZ) |n ∈ N} has rank gradient 0 if and only if the Poincaré–Lefschetz dual of the class in H1(M ; Z) corresponding to φ is represented by a fiber. This generalizes a theorem of M. Lackenby. If M is closed, we give an explicit lower bound on the rank gradient. The proof uses...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2016
ISSN: 0001-8708
DOI: 10.1016/j.aim.2016.04.019