Nonabelianness of fundamental group of flat spacetime. (English) Zbl 07889265
Summary: In the present paper, it has been obtained that the fundamental group of \(n\)-dimensional Minkowski space with the time topology contains uncountably many copies of the additive group of integers and is not abelian. The result has been first proved for \(n=2\). Thereafter, it is extended to \(n>2\) by proving that loops nonhomotopic in \(M^2\) continue to be nonhomotopic in \(M^n\) using embedding of \(M^2\) in \(M^n\) as a retract through the projection map.
MSC:
| 53Z05 | Applications of differential geometry to physics |
| 54C15 | Retraction |
| 54C25 | Embedding |
| 54J05 | Nonstandard topology |
| 55Q52 | Homotopy groups of special spaces |
| 83A99 | Special relativity |
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