منابع مشابه
Braid groups of non-orientable surfaces and the Fadell-Neuwirth short exact sequence
Let M be a compact, connected non-orientable surface without boundary and of genus g ¥ 3. We investigate the pure braid groups PnpMq of M, and in particular the possible splitting of the Fadell-Neuwirth short exact sequence 1 ÝÑ PmpMz tx1, . . . , xnuq ãÝÑ Pn mpMq p ÝÑ PnpMq ÝÑ 1, where m, n ¥ 1, and p is the homomorphism which corresponds geometrically to forgetting the last m strings. This pr...
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We study the pure braid groups Pn(RP) of the real projective plane RP2, and in particular the possible splitting of the Fadell-Neuwirth short exact sequence 1 −→ Pm(RP \ {x1, . . . , xn}) −֒→ Pn+m(RP 2) p∗ −→ Pn(RP) −→ 1, where n ≥ 2 and m ≥ 1, and p∗ is the homomorphismwhich corresponds geometrically to forgetting the last m strings. This problem is equivalent to that of the existence of a sect...
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In this paper we survey some work on representations of Bn given by the induced action on a homology module of some space. One of these, called the Lawrence-Krammer representation, recently came to prominence when it was shown to be faithful for all n. We will outline the methods used, applying them to a closely related representation for which the proof is slightly easier. The main tool is the...
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We introduce the notion of a braid group parametrized by a ring, which is defined by generators and relations and based on the geometric idea of painted braids. We show that the parametrized braid group is isomorphic to the semi-direct product of the Steinberg group (of the ring) with the classical braid group. The technical heart of the proof is the Pure Braid Lemma 2.1.1, which asserts that c...
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1973
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-11472