Pathways Workshop: Topological and Geometric Structures in Low Dimensions & Geometry and Dynamics for Discrete Subgroups of Higher Rank Lie Groups: Flipping Heegaard splittings
Presenter
January 22, 2026
Keywords:
- low-dimensional topology
- geometric structures
- homogeneous dynamics
- Anosov representations
- Higher rank Lie groups
- symmetric spaces of non- compact type
MSC:
- 57M50 - General geometric structures on low-dimensional manifolds
- 57M60 - Group actions on manifolds and cell complexes in low dimensions
- 57N16 - Geometric structures on manifolds of high or arbitrary dimension
- 57S25 - Groups acting on specific manifolds
- 22E40 - Discrete subgroups of Lie groups
- 22F30 - Homogeneous spaces
- 37E05 - Dynamical systems involving maps of the interval
- 37E10 - Dynamical systems involving maps of the circle
- 37E30 - Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
- 37E35 - Flows on surfaces
- 30F60 - Teichmüller theory for Riemann surfaces
- 32G15 - Moduli of Riemann surfaces
- Teichmüller theory (complex-analytic aspects in several variables)]
- 30F40 - Kleinian groups (aspects of compact Riemann surfaces and uniformization)
Abstract
Heegaard splittings are an old but useful tool in studying 3-manifolds. They are studied up to isotopy, up to homeomorphism, and up to stable equivalence. In this talk we review pertinent examples and highlight the interrelation of these notions of equivalence through the concept of flip genus.