The homology of Out(F_8) and Aut(F_7)

Abstract

We compute the rational homology of Out(F₈) and Aut(F₇), and several related groups. We also show that the Eisenstein classes in H₇(Aut(F₅)) and H₁₁(Aut(F₇)) are zero.

Cite

BibTeX RIS

BibTeX

@misc{grego2026homology,
  title = {{The homology of $\mathrmOut(F_8)$ and $\mathrmAut(F_7)$}},
  author = {Maroš Grego and Tomáš Vítek and Thomas Willwacher},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30872},
  eprint = {2609.30872},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30872},
}

RIS

TY  - UNPB
TI  - The homology of Out(F_8) and Aut(F_7)
AU  - Maroš Grego
AU  - Tomáš Vítek
AU  - Thomas Willwacher
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.30872
UR  - https://arxiv.org/abs/2609.30872
AB  - We compute the rational homology of Out(F_8) and Aut(F_7), and several related groups. We also show that the Eisenstein classes in H_7(Aut(F_5)) and H_11(Aut(F_7)) are zero.
ER  -