22 citations · 81 across the 11 of their papers we have counts for
14 papers
Relating VFCs on thin compactifications
Eleny-Nicoleta Ionel, Thomas H. Parker
Many moduli spaces that occur in geometric analysis admit "Fredholm-stratified thin compactifications" in the sense of [IP1] and hence admit a relative fundamental class (RFC), als…
Thin compactifications and relative fundamental classes
Eleny-Nicoleta Ionel, Thomas H. Parker
We define a notion of relative fundamental class that applies to moduli spaces in gauge theory and in symplectic Gromov-Witten theory. For universal moduli spaces over a parameter…
Corrigendum: The symplectic sum formula for Gromov-Witten invariants
Eleny-Nicoleta Ionel, Thomas H. Parker
We correct an error and an oversight in [IP]. The sign of the curvature in (8.7) is wrong, requiring a new proof of Proposition 8.1. Also, several lemmas addressed only the basic c…
The Gopakumar-Vafa formula for symplectic manifolds
Eleny-Nicoleta Ionel, Thomas H. Parker
The Gopakumar-Vafa conjecture predicts that the Gromov-Witten invariants of a Calabi-Yau 3-fold can be canonically expressed in terms of integer invariants called BPS numbers. Usin…
A natural Gromov-Witten virtual fundamental class
Eleny-Nicoleta Ionel, Thomas H. Parker
We describe a program for proving that the Gromov-Witten moduli spaces of compact symplectic manifolds carry a unique virtual fundamental class that satisfies certain naturality co…
Recursion Formulas for Spin Hurwitz Numbers
Junho Lee, Thomas H. Parker
The classical Hurwitz numbers which count coverings of a complex curve have an analog when the curve is endowed with a theta characteristic. These "spin Hurwitz numbers", recently…