Log Geometric Models for Little Disks Operads in Even Dimensions
arXiv:2503.09488 · doi:10.1017/prm.2025.10080
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.
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