arXiv subjects
Publications and source records attributed to Dun Tang.
In this paper, we establish an analog of Dijkgraaf-Witten's theorem for $g=1$ invariants in permutation-equivariant quantum K-theory. This result generalizes the findings of \cite{Tang1} and \cite{Tang2}.
In this paper, we first generalize the K-theoretic Ancestor-Descendant (AD) correspondence in \cite{perm7} to allow arbitrary permutative inputs. With this version of AD correspondence, we reconstruct K-theoretical descendant $g=0$ invariants, and $g=1$ invariants with point target space, from $1$-point invariants of the corresponding genus. In the appendix, we show that the graph of big $\mathcal{J}$ function also forms a Lagrangian cone in the permutation equivariant setting.
In this paper, we prove an analog of Dijkgraaf-Witten's theorem for $g=1$ invariants in quantum K-theory.
In this paper, we define the virtual fundamental cycle of a global Kuranishi chart as an element in the (analytic) orbispace K-homology of the virtual orbifold and verify that it defines the same invariants as those in \cite{Abouzaid23}.
In this paper, we establish equivariant mirror symmetry for the weighted projective line. This extends the results by B. Fang, C.C. Liu and Z. Zong, where the projective line was considered [{\it Geometry \& Topology} 24:2049-2092, 2017]. More precisely, we prove the equivalence of the $R$-matrices for A-model and B-model at large radius limit, and establish isomorphism for $R$-matrices for general radius. We further demonstrate that the graph sum of higher genus cases are the same for both models, hence establish equivariant mirror symmetry for the weighted projective line.