Birational invariance of tmf-classes induced by gerbes

Show that the classes in generalized tmf-cohomology induced by gerbes over an orbifold X are birational invariants of X.

Background

The paper outlines a construction sending gerbes to classes in tmf-cohomology via string orientation and maps from K(Z,3), suggesting a topological refinement of orbifold data.

They conjecture that these tmf-classes are preserved under birational transformations of orbifolds.

References

We conjecture the following. The induced classes in $\mathrm{tmf}$-generalized cohomology by gerbes over orbifolds $X$ are birational invariants.

— A Gromov-Witten approach to $G$-equivariant birational invariants (2405.07322 - Cavenaghi et al., 12 May 2024) in Section 6, after Theorem labeled ithm:tmf