Related papers: Folded galleries and moment graphs

Bordered Floer homology associates to a parametrized oriented surface a certain differential graded algebra. We study the properties of this algebra under splittings of the surface. To the circle we associate a differential graded…

We show that a compact rigid balanced braided monoidal category with enough compact projective objects gives rise to a system of mapping class group representations compatible with the gluing along marked intervals. A motivation to consider…

We give a linear algebraic classification of Auslander regular acyclic monomial algebras via the Bruhat factorisation of the Coxeter matrix. Namely, we show under mild assumptions that a monomial acyclic quiver algebra is Auslander regular…

When W is a finite Coxeter group of classical type (A, B, or D), noncrossing partitions associated to W and compatibility of almost positive roots in the associated root system are known to be modeled by certain planar diagrams. We show how…

We show that certain right-angled Coxeter groups have finite index subgroups that quotient to $\mathbb Z$ with finitely generated kernels. The proof uses Bestvina-Brady Morse theory facilitated by combinatorial arguments. We describe a…

We consider the class of those Coxeter groups for which removing from the Cayley graph any tubular neighbourhood of any wall leaves exactly two connected components. We call these Coxeter groups bipolar. They include both the virtually…

Aiming for a revival of the theory of crystallographic complex reflection groups, we compute (minimal) Coxeter-like reflection presentations for the infinite families of those non-genuine groups which satisfy Steinberg's fixed point…

Various simplicial complexes can be associated with a graph. Box complexes form an important families of such simplicial complexes and are especially useful for providing lower bounds on the chromatic number of the graph via some of their…

We follow the dual approach to Coxeter systems and show for Weyl groups a criterium which decides whether a set of reflections is generating the group depending on the root and the coroot lattice. Further we study special generating sets…

Consider a Hamiltonian action of a compact Lie group on a compact symplectic manifold. A theorem of Kirwan's says that the image of the momentum mapping intersects the positive Weyl chamber in a convex polytope. I present a new proof of…

We show the analogue of Muhlherr's [Coxeter groups in Coxeter groups, Finite Geom. and Combinatorics, Cambridge Univ. Press (1993), 277-287] for Artin-Tits monoids, and for Artin-Tits groups of spherical type. That is, the submonoid (resp.…

Alternating-sign Hopf plumbing along a tree yields fibered alternating links whose homological monodromy is, up to a sign, conjugate to some alternating-sign Coxeter transformation. Exploiting this tie, we obtain results about the location…

For a compact complex manifold, we introduce holomorphic foliations associated with certain abelian subgroups of the automorphism group. Such foliations are generalizations of holomorphic principal torus bundles. If there exists a…

Under the assumption that a defining graph of a Coxeter group admits only twists in $\mathbb{Z}_2$ and is of type FC, we prove M\"uhlherr's Twist Conjecture.

In this article, we introduce rotation groups as a common generalisation of Coxeter groups and graph products of groups (including right-angled Artin groups). We characterise algebraically these groups by presentations (periagroups) and we…

We describe edge labelings of the increasing flip graph of a subword complex on a finite Coxeter group, and study applications thereof. On the one hand, we show that they provide canonical spanning trees of the facet-ridge graph of the…

In this article we establish new positivity properties for direct images of twisted pluricanonical bundle of an algebraic fiber space. As a corollary we obtain an algebraicity criteria for holomorphic foliations which partly confirms a…

The motivation of this work is to define cohomology classes in the space of knots that are both easy to find and to evaluate, by reducing the problem to simple linear algebra. We achieve this goal by defining a combinatorial graded cochain…

We use the Fox-Neuwirth cell structure for one-point compactifications of configuration spaces as the starting point for understanding our recent calculation of the mod-two cohomology of symmetric groups. We then use that calculation to…

We construct a functor associating a cubical set to a (simple) graph. We show that cubical sets arising in this way are Kan complexes, and that the A-groups of a graph coincide with the homotopy groups of the associated Kan complex. We use…