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arXiv · 2509.08478

From Link Homology to Topological Quantum Field Theories

Paul Wedrich
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Abstract

This survey reviews recent advances connecting link homology theories to invariants of smooth 4-manifolds and extended topological quantum field theories. Starting from joint work with Morrison and Walker, I explain how functorial link homologies that satisfy additional invariance conditions become diagram-independent, give rise to braided monoidal 2-categories, extend naturally to links in the 3-sphere, and globalize to skein modules for 4-manifolds. Later developments show that these skein lasagna modules furnish invariants of embedded and immersed surfaces and admit computation via handle decompositions. I then survey structural properties, explicit computations, and applications to exotic phenomena in 4-manifold topology, and place link homology and skein lasagna modules within the framework of extended topological quantum field theories.

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Paul Wedrich. 2025-09-10. From Link Homology to Topological Quantum Field Theories. https://arxiv.org/abs/2509.08478

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