REVIEW 1 cited by
The Witten equation and its virtual fundamental cycle
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
We study a system of nonlinear elliptic PDEs associated with a quasi-homogeneous polynomial. These equations were proposed by Witten as the replacement for the Cauchy-Riemann equation in the singularity (Landau-Ginzburg) setting. We introduce a perturbation to the equation and construct a virtual cycle for the moduli space of its solutions. Then, we study the wall-crossing of the deformation of the virtual cycle under perturbation and match it to classical Picard-Lefschetz theory. An extended virtual cycle is obtained for the original equation. Finally, we prove that the extended virtual cycle satisfies a set of axioms similar to those of Gromov-Witten theory and r-spin theory.
Forward citations
Cited by 1 Pith paper
-
Finite Group Reduction of the DR/DZ Hierarchies
Finite-group reduction preserves bihamiltonian and tau structures of DR/DZ hierarchies, and two inequivalent reductions of the P¹_{2,2,2,2} CohFT give two higher-genus completions of M_{1,1}, one equivalent to genus-1...
Discussion (0). Continue with ORCID to comment.