We study some basic properties of the variety of characters in PSL(2,C) of a finitely generated group. In particular we give an interpretation of its points as characters of representations. We construct 3-manifolds whose variety of characters has arbitrarily many components that do not lift to SL(2,C). We also study the singular locus of the variety of characters of a free group.
Publié le : 2004-07-05
Classification:
Representation spaces,
variety of characters,
PSL(2,
C),
MSC: 57M50; 20C15; 57M05,
[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]
@article{hal-00425129,
author = {Heusener, Michael and Porti, Joan},
title = {The variety of characters in PSL(2,C)},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00425129}
}
Heusener, Michael; Porti, Joan. The variety of characters in PSL(2,C). HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00425129/