CATEGORICAL PROOF OF HOLOMORPHIC ATIYAH–BOTT FORMULA

@article{Kondyrev2018CATEGORICALPO,
  title={CATEGORICAL PROOF OF HOLOMORPHIC ATIYAH–BOTT FORMULA},
  author={G. Kondyrev and A. Prikhodko},
  journal={Journal of the Institute of Mathematics of Jussieu},
  year={2018},
  volume={19},
  pages={1739 - 1763}
}
Given a $2$-commutative diagram in a symmetric monoidal $(\infty ,2)$-category $\mathscr{E}$ where $X,Y\in \mathscr{E}$ are dualizable objects and $\unicode[STIX]{x1D711}$ admits a right adjoint we construct a natural morphism $\mathsf{Tr}_{\mathscr{E}}(F_{X})\xrightarrow[{}]{~~~~~}\mathsf{Tr}_{\mathscr{E}}(F_{Y})$ between the traces of $F_{X}$ and $F_{Y}$, respectively. We then apply this formalism to the case when $\mathscr{E}$ is the $(\infty ,2)$-category of $k$-linear presentable… Expand
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