q-deformed pair-of-pants and other operations on symplectic cohomology

Develop and analyze q-deformed versions of operations on symplectic cohomology—particularly the pair-of-pants product—in the deformed setting SH^*_q(M,D), providing definitions, properties, and compatibility with the thimble isomorphism and enumerative structures.

Background

Beyond the differential and thimble maps, other algebraic operations, such as the pair-of-pants product, are central in symplectic cohomology. The authors note that they have not considered q-deformations of these operations.

Constructing and understanding these operations in the deformed context would complete the algebraic picture of SH^*_q(M,D), potentially revealing deeper ties to quantum and enumerative structures relative to the divisor D.