Mathematical Sciences: Gauge Theory and 4-Manifolds

本课题的主要内容是研究光顺 利用规范不变量的连通4-流形 理论 特别是，研究者希望使用2-扭转 瞬子不变量来研究取连通和的结果 S2 x S2 利用这些挠率不变量之间的关系 使用通常的唐纳森不变量和使用Z 2-不变量 理论，研究人员希望推导出普遍的关系， 某些唐纳森不变量。 他还计划寻找 相对扭转不变量的适当设置。 这个项目与数学物理学的相互作用 两方面都要考虑。 一方面，四维流形是 在宇宙学上很重要，因为我们生活在一个由三个 空间维度和时间维度。 另一方面， 更令人惊讶的是，量子力学的概念已经导致了新的 流形的拓扑不变量

The main concern of this project is to study smooth simply connected 4-manifolds by using invariants obtained from gauge theory. In particular, the investigator wishes to use 2-torsion instanton invariants to study the result of taking connected sums with S2 x S2. Using the relation of these torsion invariants with the usual Donaldson invariants and using Z2-invariant theory, the investigator hopes to deduce universal relations for certain Donaldson invariants. He also plans to search for the proper setting for relative torsion invariants. The interactions of this project with mathematical physics go both ways. On the one hand, four-dimensional manifolds are cosmologically important, since we live in a manifold of three space dimensions and one time dimension. On the other hand, and more surprisingly, notions from quantum mechanics have led to new topological invariants of manifolds.