The real projective space in dimension 3, i.e., \(\mathbb {R}\mathbb {P}^3\) , has been embedded in various manifolds and has a large impact on Physics and Mathematics. In this chapter, we describe \(\mathbb {R}\mathbb {P}^m\) in two formal ways and analyze it with the help of topological surgery theory over time to give a clear visualization of \(\mathbb {R}\mathbb {P}^m\) , in dimension m \(=\) \(1,2,3.\)

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Real Projective Space with Topological Surgery Theory

  • Tanmay Saha

摘要

The real projective space in dimension 3, i.e., \(\mathbb {R}\mathbb {P}^3\) , has been embedded in various manifolds and has a large impact on Physics and Mathematics. In this chapter, we describe \(\mathbb {R}\mathbb {P}^m\) in two formal ways and analyze it with the help of topological surgery theory over time to give a clear visualization of \(\mathbb {R}\mathbb {P}^m\) , in dimension m \(=\) \(1,2,3.\)