Lifts of longest elements to braid groups acting on derived categories
نویسندگان
چکیده
منابع مشابه
0 Mirror symmetry and actions of braid groups on derived categories
After outlining the conjectural relationship between the conjec-tural mirror symmetry programmes of Kontsevich and Strominger-Yau-Zaslow, I will describe some natural consequences of this which are proved from scratch in joint work with Mikhail Khovanov and Paul Seidel. Namely, actions of braid groups are found on derived categories of coherent sheaves, dual to Seidel's braid group of symplecti...
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This paper gives a construction of braid group actions on the derived category of coherent sheaves on a variety X. The motivation for this is M. Kontsevich’s homological mirror conjecture, together with the occurrence of certain braid group actions in symplectic geometry. One of the main results is that when dimX ≥ 2, our braid group actions are always faithful. We describe conjectural mirror s...
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In this paper we give, for semi-simple groups without factors of type G2, a geometric construction of a braid group action on Db Coh(g̃) extending the action constructed by Bezrukavnikov, Mirković and Rumynin in the context of localization in positive characteristic. It follows that this action extends to characteristic zero, where it also has some nice representationtheoretic interpretations. T...
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To understand what a braid group is, it is easiest to visualize a braid. Consider n strands, all parallel. Consider taking the ith strand and crossing it over the very next strand. This is a braid. In fact, a braid is any sequence of crossings of the bands, provided none of the bands are self-crossing. For instance, a loop, or a band which forms a loop in the middle are not braids. Now, in orde...
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The purpose of this article is to give an exposition of certain connections between the braid groups [1, 3] and classical homotopy groups which arises in joint work of Jon Berrick, Yan-Loi Wong and the authors [8, 2, 32]. These connections emerge through several other natural contexts such as Lie algebras attached to the descending central series of pure braid groups arising as Vassiliev invari...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2014
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-2014-06104-7