Gamma-class overconvergence conjecture for quantum connections

From papers

Let MM be a monotone symplectic manifold, let KK be the coefficient field used for the rescaled quantum connection, and write Heven(M;K)H^{\mathrm{even}}(M;K) for its even cohomology. For an invertible class bHeven(M;K)b\in H^{\mathrm{even}}(M;K), the Frobenius structure has constant term

Φ0(x)=pdeg(x)/2bx.\Phi_0(x)=p^{-\operatorname{deg}(x)/2}b\smile x.

Morita's pp-adic Gamma function defines a multiplicative characteristic class Γp(TM)\Gamma_p(TM) of the tangent bundle TMTM.

Gamma-class overconvergence conjecture. For the quantum connection on any monotone symplectic manifold, the Frobenius structure with constant term above, where b=Γp(TM)b=\Gamma_p(TM), is overconvergent.

This is the concrete formulation of the paper's proposed Gamma-class correction to the Frobenius structure. The supplied text gives examples and motivation but no resolution.

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Sources & referencesView supporting material

Primary source

Shaoyun Bai, Daniel Pomerleano and Paul Seidel, “P-adic Gamma classes and overconvergent Frobenius structures for quantum connections”, arXiv:2509.26295 (2025).

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