A quantum Leray-Hirsch theorem for banded gerbes

Abstract

For a gerbe $\Y$ over a smooth proper Deligne-Mumford stack $\B$ banded by a finite group $G$, we prove a structure result on the Gromov-Witten theory of $\Y$, expressing Gromov-Witten invariants of $\Y$ in terms of Gromov-Witten invariants of $\B$ twisted by various flat $U(1)$-gerbes on $\B$. This is interpreted as a Leray-Hirsch type of result for Gromov-Witten theory of gerbes.

37 pages; v2 38 pages, to appear in JDG

References in corpus (4)

• Higher Topos Theory
• Equivariant Gromov-Witten theory of one dimensional stacks
• On Gromov-Witten theory of root gerbes
• Gromov-Witten theory of banded gerbes over schemes

Cited by in corpus (8)

• A Gromov-Witten theory for simple normal-crossing pairs without log geometry
• Orbifold Gromov--Witten theory of weighted blowups
• Double ramification cycles on the moduli spaces of admissible covers
• On the polynomiality of orbifold Gromov--Witten theory of root stacks
• On the geometry of orbifold Gromov-Witten invariants
• Double ramification cycles with orbifold targets
• On fibrations of Lie groupoids
• Mirror theorems for root stacks and relative pairs