On the SU(2,1) representation space of the Brieskorn homology spheres
Vu The Khoi
TL;DR
This paper provides a parameterization of the SU(2,1) representation space for Brieskorn homology spheres using trace coordinates, and demonstrates that the orbifold Toledo invariant cannot distinguish all connected components.
Contribution
It introduces a trace coordinate parameterization for the SU(2,1) representation space of Brieskorn spheres and analyzes the limitations of the orbifold Toledo invariant.
Findings
Trace coordinates effectively parameterize the SU(2,1) representation space.
The orbifold Toledo invariant does not distinguish all connected components.
Example showing limitations of the Toledo invariant in this context.
Abstract
In this paper, we give a parameterization of the SU(2,1) representation space of the Brieskorn homology spheres using the trace coordinates. As applications, we give an example which shows that the orbifold Toledo invariant in \cite{krebs} does not distinguish the connected components of the PU(2,1) representation space.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Algebraic Geometry and Number Theory