K(π 1)'s for Artin Groups of Finite Type

By Tom D. Brady, Colum Watt. 2000

142 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e158d0388122ce2dd335462748407c7d1b347b51

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In Artificial Intelligence

In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

Bestvina's Normal Form Complex and the Homology of Garside Groups (2002, unknown): “G R ] 7 M ar 2”
Root systems and generalized associahedra (2005, background): “The non-crossing partition lattice for W (see [7, 10]) is the interval [1, c] in the partial order (W,1) defined above.”
Finite complex reection arrangements are K(; 1) (2015, unknown): “1”
Sortable elements in infinite Coxeter groups (2008, result): “These fundamental results and others lead to further results on the lattice theory and geometry of Cambrian (semi)lattices and Cambrian fans.”
Enumerative properties of generalized associahedra (2004, unknown): “The lattice LW of noncrossing partitions associated to a finite Coxeter group W has been introduced independently in [4, 5, 6].”
Poset Topology: Tools and Applications (2006, methodology): “Interest in the absolute length order is a fairly recent development, which arose in work on the braid group [48], [49], [17].”
The language of geodesics for Garside groups (2004, background): “Sabalka [20] has shown that this is the case for B3 with respect to the common presentation B3 = 〈a, b | aba = bab〉, and he explicitly computes the complete geodesic growth series for this generating set.”
GEOMETRIC PRESENTATIONS FOR THE PURE BRAID GROUP (2006, unknown): “In 1998, Birman, Ko, and Lee [7] gave a more symmetrical presentation for the braid group on a larger generating set that has become fashionable of late (see, for example, [4], [9], [10], or [13]).”
Surveys in Combinatorics 2011: The cyclic sieving phenomenon: a survey (2010, background): “It can be shown [6, 10] that Cat(W ; 1) = #NC(W ).”
A categorification of non-crossing partitions (2013, methodology): “We recall that non-crossing partitions were introduced by Kreweras [38] and later generalised in the context of Coxeter groups by Brady and Watt [7, 8], and independently by Bessis [4]; see also Armstrong’s memoir [1].”