The rational homotopy of mapping spaces ...
Type de document :
Pré-publication ou Document de travail
Titre :
The rational homotopy of mapping spaces of E${}_n$ operads
Auteur(s) :
Fresse, Benoit [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Turchin, Victor [Auteur]
Department of Mathematics [University of Kansas]
Willwacher, Thomas [Auteur]
Institut für Mathematik [Zürich]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Turchin, Victor [Auteur]
Department of Mathematics [University of Kansas]
Willwacher, Thomas [Auteur]
Institut für Mathematik [Zürich]
Date de publication :
2017-03-17
Discipline(s) HAL :
Mathématiques [math]/Topologie algébrique [math.AT]
Résumé en anglais : [en]
We express the rational homotopy type of the mapping spaces $\mathrm{Map}^h(\mathsf D_m,\mathsf D_n^{\mathbb Q})$ of the little discs operads in terms of graph complexes. Using known facts about the graph homology this ...
Lire la suite >We express the rational homotopy type of the mapping spaces $\mathrm{Map}^h(\mathsf D_m,\mathsf D_n^{\mathbb Q})$ of the little discs operads in terms of graph complexes. Using known facts about the graph homology this allows us to compute the rational homotopy groups in low degrees, and construct infinite series of non-trivial homotopy classes in higher degrees. Furthermore we show that for $n-m>2$, the spaces $\mathrm{Map}^h(\mathsf D_m,\mathsf D_n^{\mathbb Q})$ and $\mathrm{Map}^h(\mathsf D_m,\mathsf D_n)$ are simply connected and rationally equivalent. As application we determine the rational homotopy type of the deloopings of spaces of long embeddings. Some of the results hold also for mapping spaces $\mathrm{Map}_{\leq k}^h(\mathsf D_m,\mathsf D_n^{\mathbb Q})$, $\mathrm{Map}_{\leq k}^h(\mathsf D_m,\mathsf D_n)$, $n-m\geq 2$, of the truncated little discs operads, which allows one to determine rationally the delooping of the Goodwillie-Weiss tower for the spaces of long embeddings.Lire moins >
Lire la suite >We express the rational homotopy type of the mapping spaces $\mathrm{Map}^h(\mathsf D_m,\mathsf D_n^{\mathbb Q})$ of the little discs operads in terms of graph complexes. Using known facts about the graph homology this allows us to compute the rational homotopy groups in low degrees, and construct infinite series of non-trivial homotopy classes in higher degrees. Furthermore we show that for $n-m>2$, the spaces $\mathrm{Map}^h(\mathsf D_m,\mathsf D_n^{\mathbb Q})$ and $\mathrm{Map}^h(\mathsf D_m,\mathsf D_n)$ are simply connected and rationally equivalent. As application we determine the rational homotopy type of the deloopings of spaces of long embeddings. Some of the results hold also for mapping spaces $\mathrm{Map}_{\leq k}^h(\mathsf D_m,\mathsf D_n^{\mathbb Q})$, $\mathrm{Map}_{\leq k}^h(\mathsf D_m,\mathsf D_n)$, $n-m\geq 2$, of the truncated little discs operads, which allows one to determine rationally the delooping of the Goodwillie-Weiss tower for the spaces of long embeddings.Lire moins >
Langue :
Anglais
Projet ANR :
Collections :
Source :
Fichiers
- 1703.06123
- Accès libre
- Accéder au document
- document
- Accès libre
- Accéder au document
- 1703.06123.pdf
- Accès libre
- Accéder au document