Derivative Varieties and the Pure Braid Group
نویسندگان
چکیده
منابع مشابه
Pure Virtual Braids, Resonance, and Formality
We investigate the resonance varieties, lower central series ranks, and Chen ranks of the pure virtual braid groups and their upper-triangular subgroups. As an application, we give a complete answer to the 1-formality question for this class of groups. In the process, we explore various connections between the Alexander-type invariants of a finitely generated group and several of the graded Lie...
متن کاملResearch Statement – He Wang 1 Overview
My main research interests are in algebraic topology and group theory, and their interactions with algebra, geometry and combinatorics. In early work with X. Liu [18, 19], we studied the stable homotopy theory of spheres using the May spectral sequence and the Adams spectral sequence. In a paper with X. Liu and W. Li [17], we described differentials in a certain spectral sequence converging to ...
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In 1987 Bieri, Neumann and Strebel introduced a geometric invariant for discrete groups. In this article we compute and explicitly describe the BNS-invariant for the pure braid groups. In 1987 Robert Bieri, Walter Neumann, and Ralph Strebel introduced a geometric invariant of a discrete group that is now known as its BNS invariant [BNS87]. For finitely generated groups the invariant is a subset...
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There are some similarities between cohomology of SU(2)-representation varieties of the fundamental group of some link complements and the Khovanov homology of the links. We start here a program to explain a possible source of these similarities. We introduce a symplectic manifold M with an action of the braid group B2n preserving the symplectic structure. The action allows to associate a Lagra...
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Consider the unit ball, B = D × [0, 1], containing n unknotted arcs a1, a2, . . . , an such that the boundary of each ai lies in D × {0}. The Hilden (or Wicket) group is the mapping class group of B fixing the arcs a1 ∪ a2 ∪ . . . ∪ an setwise and fixing D × {1} pointwise. This group can be considered as a subgroup of the braid group. The pure Hilden group is defined to be the intersection of t...
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