29 citations · 83 across the 18 of their papers we have counts for
21 papers
On graphic arrangement groups
Daniel C Cohen, Michael J Falk
A finite simple graph determines a quotient of the pure braid group, called a graphic arrangement group. We analyze homomorphisms of these groups defined by deletion of s…
Algebra and valuations related to the Tutte polynomial
Michael J. Falk, Joseph P. S. Kung
This is a chapter destined for the book "Handbook of the Tutte Polynomial". The chapter is a composite. The first part is a brief introduction to Orlik-Solomon algebras. The second…
Non-crossing partitions and Milnor fibers
Thomas Brady, Michael Falk, Colum Watt
For a finite real reflection group we use non-crossing partitions of type to construct finite cell complexes with the homotopy type of the Milnor fiber of the associated $W…
The Fixpoint-Iteration Algorithm for Parity Games
Florian Bruse, Michael Falk, Martin Lange
It is known that the model checking problem for the modal mu-calculus reduces to the problem of solving a parity game and vice-versa. The latter is realised by the Walukiewicz form…
BGG resolutions via configuration spaces
M. Falk, V. Schechtman, A. Varchenko
We study the blow-ups of configuration spaces. These spaces have a structure of what we call an Orlik-Solomon manifold; it allows us to compute the intersection cohomology of certa…
An equivariant discrete model for complexified arrangement complements
Emanuele Delucchi, Michael J. Falk
We define a partial ordering on the set Q = Q(M) of pairs of topes of an oriented matroid M, and show the geometric realization |Q| of the order complex of Q has the same homotopy…