BRIDGE TRISECTIONS AND CLASSICAL KNOTTED SURFACE THEORY

Authors

JASON JOSEPH, RICE UNIVERSITY
JEFFREY MEIER, WESTERN WASHINGTON UNIVERSITY
MAGGIE MILLER, STANFORD UNIVERSITY
MILLER ZUPAN, UNIVERSITY OF NEBRASKA–LINCOLNFollow

Document Type

Article

Date of this Version

8-2022

Citation

PACIFIC JOURNAL OF MATHEMATICS Vol. 319, No. 2, 2022 https://doi.org/10.2140/pjm.2022.319.343

Comments

Used by permission.

Abstract

We seek to connect ideas in the theory of bridge trisections with other wellstudied facets of classical knotted surface theory. First, we show how the normal Euler number can be computed from a tri-plane diagram, and we use this to give a trisection-theoretic proof of the Whitney–Massey theorem, which bounds the possible values of this number in terms of the Euler characteristic. Second, we describe in detail how to compute the fundamental group and related invariants from a tri-plane diagram, and we use this, together with an analysis of bridge trisections of ribbon surfaces, to produce an infinite family of knotted spheres that admit nonisotopic bridge trisections of minimal complexity.