Generators for a complex hyperbolic braid group
نویسندگان
چکیده
منابع مشابه
Generators for a Complex Hyperbolic Braid Group
We give generators for a certain complex hyperbolic braid group. That is, we remove a hyperplane arrangement from complex hyperbolic 13space, take the quotient of the remaining space by a discrete group, and find generators for the orbifold fundamental group of the quotient. These generators have the most natural form: loops corresponding to the hyperplanes which come nearest the basepoint. Our...
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We study the problem of finding generators for the fundamental group G of a space of the following sort: one removes a family of complex hyperplanes from Cn, or complex hyperbolic space CHn, or the Hermitian symmetric space for O(2, n), and then takes the quotient by a discrete group PΓ. The classical example is the braid group, but there are many similar “braid-like” groups that arise in topol...
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This paper concerns the homotopy type of hyperplane arrangements associated to infinite Coxeter groups acting as reflection groups on Cn. A long-standing conjecture states that the complement of such an arrangement should be aspherical. Some partial results on this conjecture were previously obtained by the author and M. Davis. In this paper, we extend those results to another class of Coxeter ...
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In this paper, we give a Gröbner-Shirshov basis of the braid group Bn+1 in the Artin–Garside generators. As results, we obtain a new algorithm for getting the Garside normal form, and a new proof that the braid semigroup B + n + 1 is the subsemigroup in Bn+1.
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In this paper, we obtain Gröbner-Shirshov (non-commutative Gröbner) bases for the braid groups in the Birman-Ko-Lee generators enriched by new “Garside word” δ ([2]). It gives a new algorithm for getting the Birman-KoLee Normal Form in the braid groups, and thus a new algorithm for solving the word problem in these groups.
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ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2018
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2018.22.3435