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We study the virtual Euler characteristics of sheaves over Quot schemes of curves, establishing that these invariants fit into a topological quantum field theory (TQFT) valued in Z[q]. Utilizing Quot scheme compactifications alongside the TQFT framework, we derive presentations of the small quantum K-ring of the Grassmannian. Our approach offers a new method for finding explicit formulas for quantum K-invariants.
Sinha et al. (Mon,) studied this question.