Deformation space of a non-uniform 3-dimensional real hyperbolic lattice in quaternionic hyperbolic plane

2012/02/29 by Inkang Kim, Kim, Inkang
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.1202.6672

arxiv created 2012/02/29 · arxiv updated 2012/03/01

Abstract

In this note, we study deformations of a non-uniform real hyperbolic lattice in quaternionic hyperbolic spaces. Specially we show that the representations of the fundamental group of the figure eight knot complement into PU(2,1) cannot be deformed in PSp(2,1) out of PU(2,1) up to conjugacy.

Related

• Local rigidity in quaternionic hyperbolic space
• Rank 1 deformations of non-cocompact hyperbolic lattices
• Harmonic maps and representations of non-uniform lattices of PU(m,1)
• Local quaternionic rigidity for complex hyperbolic lattices
• Figure-eight knot is always over there