Disks in trivial braid diagrams
نویسندگان
چکیده
منابع مشابه
Disks in Trivial Braid Diagrams
We show that every trivial 3-strand braid diagram contains a disk, defined as a ribbon ending in opposed crossings. Under a convenient algebraic form, the result extends to every Artin–Tits group of dihedral type, but it fails to extend to braids with 4 strands and more. The proof uses a partition of the Cayley graph and a continuity argument.
متن کاملBraids in trivial braid diagrams
We show that every trivial 3-strand braid diagram contains a disk, defined as a ribbon ending in opposed crossings. Under a convenient algebraic form, the result extends to every Artin–Tits group of dihedral type, but it fails to extend to braids with 4 strands and more. The proof uses a partition of the Cayley graph and a continuity argument.
متن کاملZariski Theorems and Diagrams for Braid Groups
Empirical properties of generating systems for complex reflection groups and their braid groups have been observed by Orlik-Solomon and Broué-Malle-Rouquier, using Shephard-Todd classification. We give a general existence result for presentations of braid groups, which partially explains and generalizes the known empirical properties. Our approach is invariant-theoretic and does not use the cla...
متن کاملHeegaard diagrams and holomorphic disks
Gromov’s theory of pseudo-holomorphic disks [39] has wide-reaching consequences in symplectic geometry and low-dimensional topology. Our aim here is to describe certain invariants for low-dimensional manifolds built on this theory. The invariants we describe here associate a graded Abelian group to each closed, oriented three-manifold Y , the Heegaard Floer homology of Y . These invariants also...
متن کاملNon-Trivial Realizations of Virtual Link Diagrams
A realization of a virtual link diagram is obtained by choosing over/under markings for each virtual crossing. Any realization can also be obtained from some representation of the virtual link. (A representation of a virtual link is a link diagram on an oriented 2dimensional surface.) We prove that if a minimal genus representation meets certain criteria then there is a minimal genus representa...
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: Topology
سال: 2004
ISSN: 0040-9383
DOI: 10.1016/j.top.2003.11.005