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On representation varieties of Artin groups,projective arrangements and the fundamental groups of smooth complex algebraic varieties.
Goldman gratefully acknowledges partial support by NSF grants DMS-9504764, DMS-9803518, DMS-0103889 and a Semester Research Award from the General Research Board of the University of Maryland in Fa...
A symplectic structure on a manifold is a closed nondegenerate exterior 2- form. The most common type of symplectic structure arises on a complex manifold as the imaginary part of a Hermitian metr...
In topology, the notions of the fundamental group and the universal cover are closely intertwined. By importing usual notions from topology into the algebraic and arithmetic setting, we construct a ...
Abstract: Examples suggest that there is a correspondence between L-spaces and 3-manifolds whose fundamental groups cannot be left-ordered. In this paper we establish the equivalence of these conditio...
Abstract: In their study of fundamental groups of one-dimensional path-connected compact metric spaces, Cannon and Conner have asked: Is there a tree-like object that might be considered the topologic...
We give a construction of hyperbolic 3-manifolds with rank two fundamental groups and report an experimental search to find such manifolds.Our manifolds are all surface bundles over the circle with ge...
There are various results that frame left-orderability of a group as a geometric property. Indeed, the fundamental group of a 3-manifold is left-orderable whenever the first Betti number is positive; ...
Using Effros-Handelman-Shen theorem and Elliott’s classification theorem of AF algebras, we show that there exists a unital simple AF algebra A with unique trace such that A K admits no trace scaling ...
A conjugation-free geometric presentation of a funda-mental group is a presentation with the natural topological gener-ators x1, . . . , xn and the cyclic relations.

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