New techniques and invariants in low-dimensional topology

该项目的目的是通过发展Seiberg-Witten理论和Floer同调的参数化和等变增强，在低维拓扑领域引入和应用新方法和不变量。由于规范理论的最新进展，这些新的精炼不变量将比现有的不变量更强大，从而能够检测到新的奇异现象。预期成果包括有效的手段，区分家庭空间，衡量其复杂性和新的障碍，他们的存在。新的不变量和技术将导致一些开放的低维拓扑问题的解决，并提高澳大利亚的声誉，作为世界领先的在这一领域。

The aim of this project is to introduce and apply new methods and invariants in the field of low-dimensional topology by developing parametrised and equivariant enhancements of Seiberg-Witten theory and Floer homology. These new refined invariants, made possible by recent advances in gauge theory, will be more powerful than existing ones, enabling the detection of new exotic phenomena. Expected outcomes include effective means for distinguishing families of spaces, measuring their complexity and new obstructions for their existence. The new invariants and techniques will lead to the resolution of some open problems in low-dimensional topology and enhance Australia's reputation as a world leader in this field.