Year: 2026
Type: preprint
Abstract: Given a cooriented branched surface $\mathcal B$ fully carrying a foliation $\mathcal F$, we use the dual graph of $\mathcal B$ to define a simplicial 1-cycle $Γ_m(\mathcal B)$ representing the Poincaré dual of the Euler class of $\mathcal F$ relative to the boundary. As an example, we complete the classification of which homology classes in the Whitehead link exterior are realisable as relative Euler classes of taut foliations. We also show how our formula generalises previous results of Lackenby and Dunfield. Finally, we observe that cooriented branched surfaces whose complement is a union of balls satisfy a Combinatorial Transverse Surface Theorem, in the sense of Landry--Minsky--Taylor.
Source: arXiv (Cornell University)
Author: Cigna, Alessandro V.
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7129265343
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