Geometric Topology
Low-dimensional topology, knots, 3-manifolds, and mapping class groups.
Geometric Topology. Low-dimensional topology, knots, 3-manifolds, and mapping class groups.
Foundations and canonical references
The standard treatments of geometric topology approach the subject from complementary angles. Thurston, Three-Dimensional Geometry and Topology (1997) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Open methodological questions for geometric topology include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1997Three-Dimensional Geometry and Topologythurston-1997
In context
Where this topic sits in the prerequisite graph. Click any node to jump.
Explore
- 01
Knot Theory
Knot invariants, Jones and HOMFLY polynomials, and Khovanov homology.
- 02
3-Manifolds and Geometrization
Thurston's geometrization and the Perelman proof.
- 03
4-Manifold Topology
Smooth and topological 4-manifolds, gauge theory, and the 11/8 conjecture.
- 04
Mapping Class Groups
Surface diffeomorphisms, Teichmüller theory, and Nielsen–Thurston classification.
- 05
Heegaard Floer Homology
Ozsváth–Szabó invariants of 3- and 4-manifolds.
- 06
Symplectic and Contact Topology
Floer homology, contact homology, and Gromov nonsqueezing.
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