Gauge-theoretic methods in the geometry of G2 manifolds.

G2流形是一类重要的Ricci平坦七维流形，目前已知其大量存在。本项目主要研究用规范论方法构造紧致G2流形的不变量。更确切地说，预期的不变量是基于所谓的G2瞬子的计数。然而，与较低维度不同，G2瞬子的数量并不期望相对于背景参数的变形是不变的，在这种情况下是G2度量。通过对周围G2流形的3-子流形上的G2瞬子和Seiberg-Witten单极子进行计数，可以得到一个沿着G2度量的合痕保持不变的不变量，本项目的重点是G2瞬子和Seiberg-Witten单极子之间的相互作用.很好地理解G2瞬子和Seiberg-Witten单极子模空间的紧化是建立这种关系的关键。

G2 manifolds constitute an important class of Ricci-flat seven-manifolds and are by now known to exist in abundance. This project is concerned with the construction of invariants of compact G2 manifolds by gauge-theoretic means. More precisely, the intended invariant is based on the count of the so called G2 instantons. However, unlike in lower dimensions, the number of G2 instantons is not expected to be invariant with respect to deformations of the background parameters, in this case the G2 metric. Conjecturally, an invariant, which remains invariant along isotopies of G2 metrics, can be obtained by counting G2 instantons together with certain Seiberg-Witten monopoles on distinguished 3-submanifolds of the ambient G2 manifold.The focus of this project is on the interplay between G2 instantons and the Seiberg-Witten monopoles. A good understanding of the compactifications of the moduli spaces of G2 instantons and the Seiberg-Witten monopoles is the key to establishing such a relationship.