arXiv research

Topological Pontryagin classes are algebraically independent in high-dimensional spaces.

Study calculates homotopy groups and derivatives for disc diffeomorphisms.

We define a cobordism category of topological manifolds and prove that if $d \neq 4$ its classifying space is weakly equivalent to $Ω^{\infty -1} MTTop(d)$, where $MTTop(d)$ is the Thom spectrum of the inverse of the canonical bundle over $BTop(d)$. We also give versions with tangential structures and boundary. The pro…

Study of Disc-structure space of compact smooth manifolds.

Study of embedding calculus using infinite operads.