Fetching the paper…

Reading the bibliography…

2015

Explicit reconstruction in quantum cohomology and K-theory

Givental, Alexander

Original
PDF
Post on X

Understand

Cohomological genus-0 Gromov-Witten invariants of a given target space can be encoded by the "descendant potential," a generating function defined on the space of power series in one variable with coefficients in the cohomology space of the target.

Replacing the coefficient space with the subspace multiplicatively generated by degree-2 classes, we explicitly reconstruct the graph of the differential of the restricted generating function from one point on it.
Using the Quantum Hirzebruch--Riemann--Roch Theorem from our joint work with Valentin Tonita, we derive a similar reconstruction formula in genus-0 quantum K-theory.
The results amplify the role of the divisor equations, and the structures of $D$-modules and $D_q$-modules in quantum cohomology and quantum K-theory with respect to Novikov's variables.

Explicit reconstruction in quantum cohomology and K-theory · Around

Built on

A. Givental. Homological geometry I. Projective hypersurfaces
1995
Earlier work this paper cites.
A. Givental. Equivariant Gromov–Witten invariants
1996
Earlier work this paper cites.
M. Kontsevich, Yu. Manin. Gromov–Witten classes, quantum cohomology, and enumerative geometry
1997
Earlier work this paper cites.
T. Coates. Riemann–Roch theorems in Gromov–Witten theory
2003
Earlier work this paper cites.
A. Givental, Y.-P. Lee. Quantum K-theory on flag manifolds, finite difference Toda lattices and quantum groups
2003
Earlier work this paper cites.

Similar

A. Givental. Symplectic geometry of Frobenius structures
2004
Cited alongside, same era.
Y.-P. Lee. Quantum K-theory I. Foundations
2004
Cited alongside, same era.
Y.-P. Lee, R. Pandharipande. A reconstruction theorem in quantum cohomology and quantum K-theory
2004
Cited alongside, same era.
T. Coates, A. Givental. Quantum cobordisms and formal group laws
2006
Cited alongside, same era.
T. Coates, A. Givental. Quantum Riemann–Roch, Lefschetz and Serre
2007
Cited alongside, same era.
I. Ciocan-Fontanine, B. Kim. Big J J -functions
Cited in the paper.
A. Givental, V. Tonita. The Hirzebruch-Riemann–Roch theorem in true genus-0 quantum K-theory
Original
Cited in the paper.
H. Iritani, T. Milanov, V. Tonita. Reconstruction and convergence in quantum K-theory via difference equations
Original
Cited in the paper.

Then

H. Iritani. Quantum D-modules and generalized mirror transformations
2008
Later among the works it cites.
A. Corti, T. Coates, H. Iritani, H.-H. Tseng. Computing twisted genus-zero Gromov-Witten invariants
2009
Later among the works it cites.
V. Tonita. A virtual Kawasaki Riemann–Roch formula
Original
2014
Later among the works it cites.
V. Tonita. Twisted orbifold Gromov–Witten invariants
Original
2014
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…