CYCLIC PRESENTATIONS OF GROUPS AND CYCLIC BRANCHED COVERINGS OF (1, 1)-KNOTS
نویسندگان
چکیده
منابع مشابه
O ct 2 00 1 Strongly - cyclic branched coverings of ( 1 , 1 ) - knots and cyclic presentations of groups ∗
We study the connections among the mapping class group of the twice punctured torus, the cyclic branched coverings of (1, 1)-knots and the cyclic presentations of groups. We give the necessary and sufficient conditions for the existence and uniqueness of the n-fold stronglycyclic branched coverings of (1, 1)-knots, through the elements of the mapping class group. We prove that every n-fold stro...
متن کاملSe p 20 01 Cyclic presentations of groups and branched cyclic coverings of ( 1 , 1
In this paper we study the connections between cyclic presentations of groups and branched cyclic coverings of (1, 1)-knots. In particular , we prove that every n-fold strongly-cyclic branched covering of a (1, 1)-knot admits a cyclic presentation for the fundamental group encoded by a Heegaard diagram of genus n.
متن کاملStrongly-cyclic branched coverings of (1,1)-knots and cyclic presentations of groups
We study the connections among the mapping class group of the twice punctured torus, the cyclic branched coverings of (1, 1)-knots and the cyclic presentations of groups. We give the necessary and sufficient conditions for the existence and uniqueness of the n-fold stronglycyclic branched coverings of (1, 1)-knots, through the elements of the mapping class group. We prove that every n-fold stro...
متن کاملSTRONGLY-CYCLIC BRANCHED COVERINGS OF KNOTS VIA (g, 1)-DECOMPOSITIONS
Strongly-cyclic branched coverings of knots are studied by using their (g, 1)-decompositions. Necessary and sufficient conditions for the existence and uniqueness of such coverings are obtained. It is also shown that their fundamental groups admit geometric g-words cyclic presentations.
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 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: Bulletin of the Korean Mathematical Society
سال: 2003
ISSN: 1015-8634
DOI: 10.4134/bkms.2003.40.1.101