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The rational homotopy type of a mapping space is a way to describe the structure of the space using the algebra of its homotopy groups and the differential graded algebra of its cochains. An L∞-model is a graded Lie algebra with a family of higher-order brackets satisfying the generalized Jacobi identity and antisymmetry. It can be used to study the rational homotopy type of a space. The nilpotency index of an L∞-model is useful in understanding a space's algebraic structure. In this paper, we compute the rational homotopy type of the component of some mapping spaces between projective spaces and determine the nilpotency index of corresponding L∞-models.
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This content will become publicly available on June 27, 2026
Kashiwara–Vergne solutions degree by degree
We show that solutions to the Kashiwara–Vergne problem can be extended degree by degree. This can be used to simplify the computation of a class of Drinfel’d associators, which under the Alekseev–Torossian conjecture, may comprise all associators. We also give a proof that the associated graded Lie algebra of the Kashiwara–Vergne group is isomorphic to the graded Kashiwara–Vergne Lie algebra.
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- Award ID(s):
- 2302664
- PAR ID:
- 10633527
- Publisher / Repository:
- Academie des Sciences Institute de France
- Date Published:
- Journal Name:
- Comptes Rendus. Mathématique
- Volume:
- 363
- Issue:
- G8
- ISSN:
- 1778-3569
- Page Range / eLocation ID:
- 777 to 789
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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