English

Log Geometric Models for Little Disks Operads in Even Dimensions

Algebraic Topology 2025-10-15 v3 Algebraic Geometry Quantum Algebra

Abstract

We construct a model for the (non-unital) S^1-framed little 2d-dimensional disks operad for any positive integer d using logarithmic geometry. We also show that the unframed little 2d-dimensional disks operad has a model which can be constructed using log schemes with virtual morphisms.

Keywords

Cite

@article{arxiv.2503.09488,
  title  = {Log Geometric Models for Little Disks Operads in Even Dimensions},
  author = {Oliver Lindström},
  journal= {arXiv preprint arXiv:2503.09488},
  year   = {2025}
}

Comments

The first version of this article incorrectly claimed that the S^1-framed little disks operad is formal in every even dimension. This claim has been removed and some minor typos have been fixed in this version. Furthermore a section (4.2) as well as some clarifying remarks and reformulations have been added to provide better geometric intuition and improve the clarity overall