15 citations · 27 across the 11 of their papers we have counts for
11 papers
Surgery on manifold operads
Xujia Chen, Connor Malin, Paolo Salvatore
We study cobordisms of a class of topological operads called ``manifold operads''. These operads are generalizations of the Fulton-MacPherson operad: an operad built from configura…
Blowdowns of the Deligne-Mumford Spaces of Real Rational Curves
Xujia Chen, Aleksey Zinger
We describe a sequence of smooth quotients of the Deligne-Mumford moduli space of real rational curves with conjugate pai…
The Cohomology Ring of the Deligne-Mumford Moduli Space of Real Rational Curves with Conjugate Marked Points
Xujia Chen, Penka Georgieva, Aleksey Zinger
It is a long-established and heavily-used fact that the integral cohomology ring of the Deligne-Mumford moduli space of (complex) rational curves is the polynomial ring on the boun…
Kontsevich's Characteristic Classes as Topological Invariants of Configuration Space Bundles
Xujia Chen
Kontsevich's characteristic classes are invariants of framed smooth fiber bundles with homology sphere fibers. It was shown by Watanabe that they can be used to distinguish smooth…
Solomon-Tukachinsky's vs. Welschinger's Open Gromov-Witten Invariants of Symplectic Sixfolds
Xujia Chen
Our previous paper describes a geometric translation of the construction of open Gromov-Witten invariants by J. Solomon and S. Tukachinsky from a perspective of -algebr…
A Geometric Depiction of Solomon-Tukachinsky's Construction of Open GW-Invariants
Xujia Chen
The 2016 papers of J. Solomon and S. Tukachinsky use bounding chains in Fukaya's -algebras to define numerical disk counts relative to a Lagrangian under certain regula…
Spin/Pin-Structures and Real Enumerative Geometry
Xujia Chen, Aleksey Zinger
The present, partly expository, monograph consists of three parts. The first part treats Spin- and Pin-structures from three different perspectives and shows them to be suitably eq…
WDVV-Type Relations for Disk Gromov-Witten Invariants in Dimension 6
Xujia Chen, Aleksey Zinger
The first author's previous work established Solomon's WDVV-type relations for Welschinger's invariant curve counts in real symplectic fourfolds by lifting geometric relations over…
WDVV-Type Relations for Welschinger's Invariants: Applications
Xujia Chen, Aleksey Zinger
We first recall Solomon's relations for Welschinger's invariants counting real curves in real symplectic fourfolds, announced in \cite{Jake2} and established in \cite{RealWDVV}, an…
Steenrod Pseudocycles, Lifted Cobordisms, and Solomon's Relations for Welschinger's Invariants
Xujia Chen
We establish two WDVV-style relations for the disk invariants of real symplectic fourfolds by implementing Georgieva's suggestion to lift homology relations from the Deligne-Mumfor…
Jenkins-Strebel Differentials on the Riemann Sphere with Four Simple Poles
Xujia Chen, Bin Xu
A celebrated and deep theorem in the theory of Riemann surfaces states the existence and uniqueness of the Jenkins-Strebel differentials on a Riemann surface under some conditions,…