解析・幾何セミナー (Salvatori Niccolo 氏)

Closed odd-dimensional manifolds with trivial cohomology can be distinguished by their analytic torsion (a secondary topological invariant introduced by Ray and Singer in 1971 that coincides with the Reidemeister torsion). In this talk, we will show that analytic torsion can be equivalently obtained by the (quasi) trace of a log-polyhomogenous operator and, by the use of Wodzicki's residue, we will define and study an exotic torsions: the residue analytic torsion, which turns out to be a smooth invariant in some occasions, with properties that are complementary to those of the analytic torsion. Then, we will define the new concept of LogTQFT and use the residue torsion to provide an example. If time allows, we will present a generalization of the previous results to families of closed manifolds and to manifolds with boundary.