arXiv Open Access 2024

Formality of $\mathbb{E}_n$-algebras and cochains on spheres

Gijs Heuts Markus Land

Lihat Sumber

Abstrak

We study the loop and suspension functors on the category of augmented $\mathbb{E}_n$-algebras. One application is to the formality of the cochain algebra of the $n$-sphere. We show that it is formal as an $\mathbb{E}_n$-algebra, also with coefficients in general commutative ring spectra, but rarely $\mathbb{E}_{n+1}$-formal unless the coefficients are rational. Along the way we show that the free functor from operads in spectra to monads in spectra is fully faithful on a nice subcategory of operads which in particular contains the stable $\mathbb{E}_n$-operads for finite $n$. We use this to interpret our results on loop and suspension functors of augmented algebras in operadic terms.

Topik & Kata Kunci

math.AT

Penulis (2)

Gijs Heuts

Markus Land

Format Sitasi

APA MLA BibTeX

Heuts, G., Land, M. (2024). Formality of $\mathbb{E}_n$-algebras and cochains on spheres. https://arxiv.org/abs/2407.00790

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓