What question did this study set out to answer?

The central aim is to explore computable invariants in low-dimensional topology and their implications.

March 21, 2026Open Access

MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation

Key Points

The central aim is to explore computable invariants in low-dimensional topology and their implications.
Discussion sessions among experts
Focus on various aspects of low-dimensional topology
Examination of specific topics like random knots and clasp number knots
Study of algebraic models and their applications
Identified key computable invariants relevant to spatial graphs and knots
Discussed implications of Poincaré duality complexes in dimension 4
Explored the relationship between topological features and volume in three-dimensional spaces

Abstract

The MATRIX-MFO tandem workshop addressed several research questions in low-dimensional topology and related areas. The format of the workshop consisted primarily of discussion sessions focusing on computable invariants of colored spatial graphs, random knots, small clasp number knots, algebraic models for Poincaré duality complexes in dimension 4, and the topological volume of the three-torus.

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MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation

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Abstract

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