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Low-Dimensional Topology

Low-Dimensional Session #1 #1

Subevent of Low-Dimensional Session #1

Central Time (US & Canada)

Ideal Triangulations and Once-Punctured Surface Bundles | Birch Bryant

Starts at: 2025-08-11 10:00AM

Ends at: 2025-08-11 10:25AM

Ideal Triangulations and Once-Punctured Surface Bundles

Birch Bryant ⟨bbryant3@una.edu⟩

Abstract:

A well-known result of Walsh states that if T is an ideal triangulation of an atoroidal, acylindrical, irreducible, compact 3-manifold with torus boundary components and T has essential edges, then every properly embedded, two-sided, incompressible surface S is isotopic to a spun-normal surface in T unless S is isotopic to a fiber or virtual fiber. For a given manifold M that fibers over S1, it was previously unknown whether there exists an ideal triangulation in which the fiber appears as a spun-normal surface. We prove that such a triangulation exists and give an algorithm to construct the ideal triangulation provided M has a single boundary component.

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