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4 results for “Zariski-density”

On TQFT representations of mapping class groups with boundarymath.GT

Study TQFT representations for surfaces with boundary, showing irreducibility at prime roots of unity and Zariski density for transcendental parameters.

problem Understanding TQFT representations of mapping class groups with boundary.

method Examined TQFT representations for surfaces with boundary associated with

SU(2)

gauge group or $U_q(\Sl(2))$ quantum group.

result At prime roots of unity, representations are irreducible; for transcendental parameters, the image of mapping class groups is Zariski dense.

TQFT mapping class groups surface topology irreducibility Zariski density

2018-09-18abs ↗pdf ↗

Density of Zariski density for surface groupsmath.DG

We show that a surface group contained in a reductive real algebraic group can be deformed to become Zariski dense, unless its Zariski closure acts transitively on a Hermitian symmetric space of tube type. This is a kind of converse to a rigidity result of Burger, Iozzi and Wienhard.

2010-09-12abs ↗pdf ↗

Boundary maps and maximal representations on infinite dimensional Hermitian symmetric spacesmath.GR

Maximal representations in infinite dimensional Hermitian spaces are studied with boundary maps.

problem Characterizing maximal representations in infinite dimensional Hermitian symmetric spaces.

method Definition of Toledo number, study of boundary maps, geometric constructions.

result Existence and non-existence conditions for maximal representations.

maximal representations infinite dimensional Hermitian spaces boundary maps Zariski-density toledo number

2018-10-24abs ↗pdf ↗

Zariski density and finite quotients of mapping class groupsmath.GR

Our main result is that the image of the quantum representation of a central extension of the mapping class group of the genus $g\geq 3$ closed orientable surface at a prime $p\geq 5$ is a Zariski dense discrete subgroup of some higher rank algebraic semi-simple Lie group $\mathbb G_p$ defined over $\Q$. As an applicat…

2011-06-21abs ↗pdf ↗