Geometry & Geometric Analysis Seminar
The Geometry and Geometric Analysis (GAGA) Seminar is an opportunity for geometers, topologists, and others from TCU and other campuses to learn about new topics of mutual interest. GAGA meets most weeks during the school year. You can find notes from past talks at the GAGA Note Repository, located in a secure off-campus location.
The next meeting of GAGA will be Tuesday, April 29 from 4 to 5 pm in Tucker Technology Center (TUC) 243. Igor Prokhorenkov will lecture on "Reidemeister and Analytic Torsion."
Abstract: The Reidemeister torsion (R-torsion) is a topological invariant that generalizes the Euler characteristic in the case where the Euler characteristic vanishes. Certain lens spaces were known to be homotopy equivalent, and it was conjectured that some of them are not homeomorphic. The Reidemeister torsion was used to prove this conjecture. Ray and Singer introduced an analytic analog of R-torsion utilizing the Laplace operator on differential forms. It was further shown that this is the same as the R-torsion, in spite of the fact that its definition uses the metric and smooth structure of the manifold. This sequence of lectures will be given at an elementary level so that graduate students (but not necessarily faculty) may be able to understand them.