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A polynomial invariant of a homology 3-sphere defined by Reidemeister torsion
SPEAKER  |  Teruaki Kitano
INSTITUTE  |  
DATE  |  May 10(Wed), 2017
TIME  |  10:00
PLACE  |  8101
Keyword  |  
Download  |  
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.
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