A polynomial invariant of a homology 3-sphere defined by Reidemeister torsion
SPEAKER | Teruaki Kitano
DATE | May 10(Wed), 2017
TIME | 10:00
PLACE | 8101
ABSTRACT | In the end of 1980s Dennis Johnson studied Reidemeister torsion for a homology 3-sphere
from the view point of Casson invariant, as follows.
Let M be a homology 3-sphere with a fixed Heegaard splitting. Johnson gave volume forms on the spaces of conjugacy classes of SU(2)-irreducible representations for the closed surface and handle bodies. Under some assumption, he considered a weight for each conjugacy class and proved this weight is equal to Reidemeister torsion of M for the corresponding irreducible representation composed with the adjoint representation.
Further he proposed to study polynomials whose zeros are the values of Reidemeister torsion of M for several settings.
In this talk, for SL(2;C)-representation, we would like to explain Johnson theory and show some formulas, examples, and properties, for Brieskorn homology spheres and surgeried manifolds along the figure-eight knot. Some of them concern a joint work with Anh Tran.