Rigidity of representations in SO(4, 1) for Dehn fillings on 2-bridge knots

Stefano Francaviglia; Joan Porti

doi:10.2140/pjm.2008.238.249

Rigidity of representations in SO(4, 1) for Dehn fillings on 2-bridge knots

Stefano Francaviglia, Joan Porti

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

2 Citations (Scopus)

Abstract

We prove that, for a hyperbolic two-bridge knot, infinitely many Dehn fillings are rigid in SO0(4, 1). Here rigidity means that any discrete and faithful representation in SO0(4, 1) is conjugate to the holonomy representation in SO0(3, 1). We also show local rigidity for almost all Dehn fillings.

Original language	English
Pages (from-to)	249-274
Journal	Pacific Journal of Mathematics
Volume	238
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2008.238.249
Publication status	Published - 1 Dec 2008

Keywords

Cuspidal cohomology
Dehn filling
Fuchsian representation
Global rigidity
Two-bridge knot

Access to Document

10.2140/pjm.2008.238.249

Cite this

@article{66288991397646f983b6a368db586da9,

title = "Rigidity of representations in SO(4, 1) for Dehn fillings on 2-bridge knots",

abstract = "We prove that, for a hyperbolic two-bridge knot, infinitely many Dehn fillings are rigid in SO0(4, 1). Here rigidity means that any discrete and faithful representation in SO0(4, 1) is conjugate to the holonomy representation in SO0(3, 1). We also show local rigidity for almost all Dehn fillings.",

keywords = "Cuspidal cohomology, Dehn filling, Fuchsian representation, Global rigidity, Two-bridge knot",

author = "Stefano Francaviglia and Joan Porti",

year = "2008",

month = dec,

day = "1",

doi = "10.2140/pjm.2008.238.249",

language = "English",

volume = "238",

pages = "249--274",

journal = "Pacific Journal of Mathematics",

issn = "0030-8730",

publisher = "University of California, Berkeley",

number = "2",

}

TY - JOUR

T1 - Rigidity of representations in SO(4, 1) for Dehn fillings on 2-bridge knots

AU - Francaviglia, Stefano

AU - Porti, Joan

PY - 2008/12/1

Y1 - 2008/12/1

N2 - We prove that, for a hyperbolic two-bridge knot, infinitely many Dehn fillings are rigid in SO0(4, 1). Here rigidity means that any discrete and faithful representation in SO0(4, 1) is conjugate to the holonomy representation in SO0(3, 1). We also show local rigidity for almost all Dehn fillings.

AB - We prove that, for a hyperbolic two-bridge knot, infinitely many Dehn fillings are rigid in SO0(4, 1). Here rigidity means that any discrete and faithful representation in SO0(4, 1) is conjugate to the holonomy representation in SO0(3, 1). We also show local rigidity for almost all Dehn fillings.

KW - Cuspidal cohomology

KW - Dehn filling

KW - Fuchsian representation

KW - Global rigidity

KW - Two-bridge knot

U2 - 10.2140/pjm.2008.238.249

DO - 10.2140/pjm.2008.238.249

M3 - Article

SN - 0030-8730

VL - 238

SP - 249

EP - 274

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 2

ER -

Rigidity of representations in SO(4, 1) for Dehn fillings on 2-bridge knots

Abstract

Keywords

Access to Document

Fingerprint

Cite this