# Categorification of invariants in gauge theory and symplectic geometry

@article{Fukaya2017CategorificationOI, title={Categorification of invariants in gauge theory and symplectic geometry}, author={Kenji Fukaya}, journal={Japanese Journal of Mathematics}, year={2017}, volume={13}, pages={1-65} }

This is a mixture of survey article and research announcement. We discuss instanton Floer homology for 3 manifolds with boundary. We also discuss a categorification of the Lagrangian Floer theory using the unobstructed immersed Lagrangian correspondence as a morphism in the category of symplectic manifolds. During the year 1998–2012, those problems have been studied emphasizing the ideas from analysis such as degeneration and adiabatic limit (instanton Floer homology) and strip shrinking…

## 5 Citations

### Categorification of invariants in gauge theory and symplectic geometry

- MathematicsJapanese Journal of Mathematics
- 2017

This is a mixture of survey article and research announcement. We discuss instanton Floer homology for 3 manifolds with boundary. We also discuss a categorification of the Lagrangian Floer theory…

### Atiyah-Floer conjecture: A formulation, a strategy of proof and generalizations

- MathematicsProceedings of Symposia in Pure Mathematics
- 2018

Around 1988, Floer introduced two important theories: instanton Floer homology as invariants of 3-manifolds and Lagrangian Floer homology as invariants of pairs of Lagrangians in symplectic…

### T-equivariant disc potentials for toric Calabi-Yau manifolds

- Mathematics
- 2019

We study the equivariant disc potentials for immersed SYZ fibers in toric Calabi-Yau manifolds. The immersed Lagrangians play a crucial role in the partial compactification of the SYZ mirrors.…

### Unobstructed immersed Lagrangian correspondence and filtered A infinity functor

- Mathematics
- 2017

In this paper we construct a 2-functor from the unobstructed immersed Weinstein category to the category of all filtered A infinity categories. We consider arbitrary (compact) symplectic manifolds…

### A compactness theorem for SO(3) anti-self-dual equation with translation symmetry

- MathematicsAdvances in Mathematics
- 2022

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Around 1988, Floer introduced two important theories: instanton Floer homology as invariants of 3-manifolds and Lagrangian Floer homology as invariants of pairs of Lagrangians in symplectic…

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