分野別セミナー

九大幾何学・トポロジー合同セミナー

【講演要旨】First, I will recall the leafwise Hodge decomposition for Riemannian foliations,
obtained in collaboration with Yuri Kordyukov in 2000. Next, I will recall
two examples of foliations, by Guillemin and by Deninger and Singhoff,
where the leafwise Hodge decomposition fails, and even a trace formula
for foliated flows fails in the second example. Finally, I’ll explain a different
type of leafwise Hodge decomposition that is true in those examples, and
how an additional term for the trace formula appears, making it true in
the second example. This is a work in progress.