## Geometry & Topology

### Pixton's double ramification cycle relations

#### Abstract

We prove a conjecture of Pixton, namely that his proposed formula for the double ramification cycle on $M̄g,n$ vanishes in codimension beyond $g$. This yields a collection of tautological relations in the Chow ring of $M̄g,n$. We describe, furthermore, how these relations can be obtained from Pixton’s $3$–spin relations via localization on the moduli space of stable maps to an orbifold projective line.

#### Article information

Source
Geom. Topol., Volume 22, Number 2 (2018), 1069-1108.

Dates
Revised: 20 April 2017
Accepted: 24 May 2017
First available in Project Euclid: 1 February 2018

https://projecteuclid.org/euclid.gt/1517454115

Digital Object Identifier
doi:10.2140/gt.2018.22.1069

Mathematical Reviews number (MathSciNet)
MR3748684

Zentralblatt MATH identifier
06828604

#### Citation

Clader, Emily; Janda, Felix. Pixton's double ramification cycle relations. Geom. Topol. 22 (2018), no. 2, 1069--1108. doi:10.2140/gt.2018.22.1069. https://projecteuclid.org/euclid.gt/1517454115

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