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On representation varieties of Artin groups,projective arrangements and the fundamental groups of smooth complex algebraic varieties
Artin groups,projective arrangements fundamental groups smooth complex algebraic varieties
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2015/10/14
On representation varieties of Artin groups,projective arrangements and the fundamental groups of smooth complex algebraic varieties.
Rank One Higgs Bundles and Representations of Fundamental Groups of Riemann Surfaces
Higgs Bundles Fundamental Groups
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2015/9/29
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...
The Symplectic Nature of Fundamental Groups of Surfaces
Surfaces Symplectic Nature
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2015/9/29
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...
Universal covering spaces and fundamental groups in algebraic geometry as schemes
algebraic geometry fundamental groups
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2015/7/14
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 ...
On L-spaces and left-orderable fundamental groups
left-orderable fundamental groups Geometric Topology
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2011/9/20
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...
Combinatorial R-trees as generalized Cayley graphs for fundamental groups of one-dimensional spaces
R-tree generalized Cayley graph one-dimensional space
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2011/8/29
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...
Constructions of surface bundles with rank two fundamental groups
Heegaard genus 2-generator group surface bundle
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2011/2/28
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...
Left-orderable fundamental groups and Dehn surgery
Left-orderable fundamental groups Dehn surgery
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2010/12/9
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; ...
A note on trace scaling actions and fundamental groups of $C^*$-algebras
Fundamental group Trace scaling action Dimension group
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2010/12/1
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 fundamental groups of arrangements II: Expansion and some properties
conjugation-free geometric presentation of fundamental groups some properties
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2010/12/1
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.