Tadayuki Watanabe

Obstructions for \(\pi_1\) of the space of pseudo-isotopies of disks in non-stable range

video: comming soon.
abstract:
We study the fundamental group of the space of pseudo-isotopies \(\mathcal{C}(D^d)\) of odd-dimensional disks by using parametrized Morse theory. In particular we introduce some algebraic obstructions for trivializing pseudo-isotopy fiber bundles over \(S^2\) and show that if the obstructions for an element \(\xi\) of \(\pi_1\mathcal{C}(D^d)\otimes\mathbb{Q}\) vanish, then \(\xi\) is trivial when \(d\geq 7\) odd, and \(\xi\) can be represented by a family of framed embeddings of 2-spheres in \(\mathbb{R}^5\) and some simple pattern parametrized by some abelian group when \(d=5\).