Enumeration of Branched Coverings of Nonorientable Surfaces With Cyclic Branch Points
نویسندگان
چکیده
منابع مشابه
Enumeration of Branched Coverings of Nonorientable Surfaces With Cyclic Branch Points
Abstract. In this paper, n-fold branched coverings of a closed nonorientable surface S of genus p with r ≥ 1 cyclic branch points (that is, such that all ramification points over them are of multiplicity n) are considered. The number Np, r(n) of such coverings up to equivalence is evaluated explicitly in a closed form (without using any complicated functions such as irreducible characters of th...
متن کاملEnumeration of the Branched Zp-Coverings of Closed Surfaces
A continuous function p : S̃ → S between two surfaces S̃ and S is called a branched covering if there exists a finite set B in S such that the restriction of p to S̃ − p−1(B), p | S̃−p−1(B) : S̃− p −1(B)→ S− B, is a covering projection in the usual sense. The smallest set B of S which has this property is called the branch set. A branched covering p : S̃ → S is regular if there exists a (finite) grou...
متن کاملOn cyclic branched coverings of prime knots
The Torelli subgroup of Out(Fn) Mladen Bestvina, Utah The group in the title is the kernel of the natural map Out(Fn) –> GLn(Z). As for the classical mapping class group counterparts (except for the work of Mess in low genus), the basic features such as the dimension and finiteness properties are unknown. I will describe an approach to an understanding to these groups that leads to a complete s...
متن کاملEnumerating branched coverings over surfaces with boundaries
The number of nonisomorphic n-fold branched coverings over a given surface with a boundary is determined by the number of nonisomorphic n-fold graph coverings over a suitable bouquet of circles. A similar enumeration can be done for regular branched coverings. Some explicit formulae for enumerations are also obtained. © 2003 Elsevier Ltd. All rights reserved. MSC 2000: 05C10; 05C30; 57M12
متن کاملOn the existence of branched coverings between surfaces with prescribed branch data
Given a branched covering between closed connected surfaces, one can easily establish some relations between the Euler characteristic and orientability of the involved surfaces, the degree of the covering, the number of branching points, and the local degrees at these points. These relations can therefore be regarded as necessary conditions for the existence of the covering. A classical problem...
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: SIAM Journal on Discrete Mathematics
سال: 2005
ISSN: 0895-4801,1095-7146
DOI: 10.1137/s0895480103424043