From Link Homology to Topological Quantum Field Theories
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912629030649856 |
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| author | Wedrich, Paul |
| author_facet | Wedrich, Paul |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08478 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Link Homology to Topological Quantum Field Theories Wedrich, Paul Quantum Algebra Category Theory Geometric Topology 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. |
| title | From Link Homology to Topological Quantum Field Theories |
| topic | Quantum Algebra Category Theory Geometric Topology |
| url | https://arxiv.org/abs/2509.08478 |