Combinatorial 3-manifolds with a cyclic automorphism group
ثبت نشده
چکیده
In this article we substantially extend the classification of combinatorial 3-manifolds with cyclic automorphism group up to 22 vertices. Moreover, several combinatorial criteria are given to decide, whether a cyclic combinatorial d-manifold can be generalized to an infinite family of such complexes together with a construction principle in the case that such a family exist. In addition, a new infinite series of cyclic neighborly combinatorial lens spaces of infinitely many distinct topological types is presented. MSC 2010: 57Q15; 57N10; 57M05
منابع مشابه
Linfan Mao Automorphism Groups of Maps, Surfaces and Smarandache Geometries
A combinatorial map is a connected topological graph cellularly embeddedin a surface. This monograph concentrates on the automorphism groupof a map, which is related to the automorphism groups of a Klein surfaceand a Smarandache manifold, also applied to the enumeration of unrootedmaps on orientable and non-orientable surfaces. A number of results for theautomorphism groups ...
متن کاملOn the Automorphism Groups and Equivalence of Cyclic Combinatorial Objects
We determine the permutation groups that arise as the automorphism groups of cyclic combinatorial objects. As special cases we classify the automorphism groups of cyclic codes. We also give the permutations by which two cyclic combinatorial objects on p elements are equivalent.
متن کاملDegree-regular triangulations of torus and Klein bottle
A combinatorial 2-manifold is called weakly regular if the action of its automorphism group on its vertices is transitive. A combinatorial 2-manifold is called degree-regular if each of its vertices have the same degree. Clearly, a weakly regular combinatorial 2-manifold is degree-regular. In [5], Lutz has classified all the weakly-regular combinatorial 2-manifolds on at most 15 vertices, among...
متن کاملSome combinatorial aspects of finite Hamiltonian groups
In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite H...
متن کاملOn the number of optimal surfaces
Let X be a closed oriented Riemann surface of genus ≥ 2 of constant negative curvature −1. A surface containing a disk of maximal radius is an optimal surface. This paper gives exact formulae for the number of optimal surfaces of genus ≥ 4 up to orientation-preserving isometry. We show that the automorphism group of such a surface is always cyclic of order 1, 2, 3 or 6. We also describe a combi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011