Geometry of Principal Fiber Bundles -
Homogeneous Spaces, Invariant Connections, Gauge Theory, and Beyond
Almost two years ago, together with Henrik Naujoks and Marvin Theiß, we embarked on our journey of turning `The ANT Project' into reality. This is a concise treatise on all the differential geometry linked to principal fiber bundles, with a particular focus on the fascinating world of invariant connections, holonomy, gauge fields and their applications in mathematical physics.
The first versions were lecture notes from my differential geometry courses and some very old handwritten notes by Thomas Friedrich. The next crucial building blocks were the master's theses of Henrik and Marvin. One of our goals is to cover all the material on these topics included in the two volumes by Kobayashi and Nomizu, but in an updated, modern language with a user-friendly exposition.
For now, we can only offer you the table of contents for download, to give you an idea of what it will be like. If you are interested in any of the topics covered, please email us. We are happy to share preliminary versions in exchange for feedback, provided you are willing to be patient with a text that is far from finished. We cannot yet predict when it will be finished, as we are all busy with other duties and activities. We usually collaborate on `The ANT' through book-writing retreats.