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July 13, 2026Inventiones mathematicae3 citationsOpen Access

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

MKManuel KrannichOROscar Randal‐Williams

Key Points

  • The aim is to compute the rational homotopy groups of diffeomorphisms of closed discs and analyze the rational homotopy type of BTop.
  • Computed homotopy groups for diffeomorphisms of closed d-dimensional discs fixing the boundary.
  • Determined optimal rational concordance stable range for high-dimensional discs.
  • Calculated the second rational derivative of the functor BTop(-) using Weiss' orthogonal calculus.
  • Identified rational homotopy groups in degrees up to approximately 3/2d.
  • Described the rational homotopy type of BTop(d) within a specified range.
  • Calculated the second Weiss derivative of the functor BTop(-) with detailed analysis.

Abstract

Abstract We compute the rational homotopy groups in degrees up to approximately 32d 3 2 d of the group of diffeomorphisms of a closed d 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 B Top (d) B Top (d) in a range, and calculate the second rational derivative of the functor B Top (-) B Top (−) in the sense of Weiss’ orthogonal calculus.

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Cite This Study

Krannich et al. (2026) studied this question.

synapsesocial.com/papers/6a547f6d475c38bf615a506ahttps://doi.org/10.1007/s00222-026-01436-2
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