Tropical Todd genus conjecture for compact tropical manifolds

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Let XX be a compact tropical manifold of dimension nn. The Todd class of XX is obtained from the formal power series in its Chern classes by substituting ck=csm⁡n−k(X)c_k=\operatorname{csm}_{n-k}(X), and let Todd⁡d(X)\operatorname{Todd}_d(X) denote its degree dd part. Tropical Todd genus conjecture. One has

χ(X)=deg⁡Todd⁡n(X).\chi(X)=\deg \operatorname{Todd}_n(X).

This conjecture generalizes the classical Noether formula to compact tropical manifolds in arbitrary dimension using tropical Chern–Schwartz–MacPherson classes and the tropical Todd class.

References

Primary source

Lucía López de Medrano, Felipe Rincón and Kris Shaw, “Chern Classes of Tropical Manifolds”, arXiv:2309.00229 (2023).

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