Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published July 2016 | Submitted
Book Section - Chapter Open

Moduli Operad over F_1

Abstract

In this paper we answer a question raised in [25], Sec. 4, by showing that the genus zero moduli operad {M_(0,n+1)} can be endowed with natural descent data that allow it to be considered as the lift to Spec Z of an operad over F_1. The relevant descent data are based on a notion of constructible sets and constructible functions over F_1, which describes suitable differences of torifications with a positivity condition on the class in the Grothendieck ring. More generally, we do the same for the operads {T_(d,n+1)} (whose components were) introduced in [5]. Finally, we describe a blueprint structure on {M_(0,n)} and we discuss from this perspective the genus zero boundary modular operad {M^0_(g,n+1)}.

Additional Information

© 2016 EMS Publishing House. The second author acknowledges support and hospitality of the Max Planck Institute and the Mathematical Sciences Research Institute and support from NSF grants DMS-0901221, DMS-1007207, DMS-1201512, PHY-1205440. We thank Paolo Aluffi, Tom Graber and Oliver Lorscheid for constructive criticism, useful comments and discussions.

Attached Files

Submitted - 1302.6526.pdf

Files

1302.6526.pdf
Files (383.8 kB)
Name Size Download all
md5:1c96651c125d5f5387fc865afcffcb9e
383.8 kB Preview Download

Additional details

Created:
August 20, 2023
Modified:
March 5, 2024