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arxiv: 2109.03500 · v2 · pith:GUM5RXLBnew · submitted 2021-09-08 · 🧮 math.AT · math.GT

Diffeomorphisms of discs and the second Weiss derivative of BTop(-)

Manuel Krannich , Oscar Randal-Williams This is my paper
classification 🧮 math.AT math.GT
keywords rationalbtopderivativediffeomorphismsdiscshomotopyrangesecond
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We compute the rational homotopy groups in degrees up to approximately $\tfrac{3}{2}$d of the group of diffeomorphisms of a closed d-dimensional disc fixing the boundary. Based on this we determine the optimal rational concordance stable range for high-dimensional discs, describe the rational homotopy type of BTop(d) in a range, and calculate the second rational derivative of the functor BTop(-) in the sense of Weiss' orthogonal calculus.

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