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Peer-reviewedCC BYInventiones mathematicae

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

  • Manuel Krannich1
  • Oscar Randal‐Williams2
  1. 1Department of Mathematics, Karlsruhe Institute of Technology, 76131, Karlsruhe, Germany
  2. 2Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WB, UK
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Abstract

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

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Cite

BibTeXRIS
BibTeX
@article{krannich2026diffeomorphisms,
  title = {{Diffeomorphisms of discs and the second Weiss derivative of BTop(–)}},
  author = {Manuel Krannich and Oscar Randal‐Williams},
  journal = {Inventiones mathematicae},
  year = {2026},
  month = jul,
  doi = {10.1007/s00222-026-01436-2},
  url = {https://doi.org/10.1007/s00222-026-01436-2},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Diffeomorphisms of discs and the second Weiss derivative of BTop(–)
AU  - Manuel Krannich
AU  - Oscar Randal‐Williams
PY  - 2026
DA  - 2026/07/10
JO  - Inventiones mathematicae
DO  - 10.1007/s00222-026-01436-2
UR  - https://doi.org/10.1007/s00222-026-01436-2
AB  - We compute the rational homotopy groups in degrees up to approximately 3/2d 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 BTop(d) B Top ( d ) in a range, and calculate the second rational derivative of the functor BTop(−) B Top ( − ) in the sense of Weiss’ orthogonal calculus.
SN  - 0020-9910
SN  - 1432-1297
ER  -