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 \(d=5\).
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