The discussion centers around the motivation for physicists to learn topology, its applications in various fields of physics, and the insights topology may provide into physical concepts, particularly in relation to the shape of spacetime and global properties of physical systems.
Participants express a range of views on the significance of topology in physics, with some agreeing on its importance for global properties of spacetime while others remain uncertain about its distinction from differential geometry. The discussion does not reach a consensus on the extent of topology's applications or its foundational role in physics.
The discussion highlights limitations in participants' mathematical backgrounds and varying levels of familiarity with topology, which may affect their interpretations and contributions.
quasar987 said:I was under the impression that only differential geometry was involved in calculating the shape of space time. Can anyone confirm what Danger said?
This intervention is not a professional one and many other people could give a better answer to your question than me. But if you think to the notion of parallel transport and to its consequence, the Berry's phase for example, you get a first concrete application of the indirect effect of the topology on physical phenomenon. In my non-specialist mind, geometry and topology are notions very closed together even if any specialist will immediately contradicts my point of view. Hope I could help you!quasar987 said:What is the motivation for a physicist to learn topology?
Are there fields of physics that make explicit use of the concept of topology? (which ones)
Do the ideas of topology give any insights into any topic of physics?
etc.