منابع مشابه
Toroidal Embeddings of Right Groups
In this note we study embeddings of Cayley graphs of right groups on surfaces. We characterize those right groups which have a toroidal but no planar Cayley graph, such that the generating system of the right group has a minimal generating system of the group as a factor.
متن کاملSeparating Cycles in Doubly Toroidal Embeddings
We show that every 4-representative graph embedding in the double torus contains a noncontractible cycle which separates the surface into two pieces. This improves a result of Zha and Zhao for general orientable surfaces, in which the same conclusion holds for 6-representative graph embeddings. Noncontractible separating cycles have been studied because they provide a way to do induction on the...
متن کاملOn the flexibility of toroidal embeddings
Two embeddings Ψ1 and Ψ2 of a graph G in a surface Σ are equivalent if there is a homeomorphism of Σ to itself carrying Ψ1 to Ψ2. In this paper, we classify the flexibility of embeddings in the torus with representativity at least 4. We show that if a graph G has an embedding Ψ in the torus with representativity at least 4, then one of the following holds: (i) Ψ is the unique embedding of G in ...
متن کاملLinking 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 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: European Journal of Mathematics
سال: 2015
ISSN: 2199-675X,2199-6768
DOI: 10.1007/s40879-015-0084-y