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PreprintarXiv licencearXiv

Projective Braids in ℝP3

  • Aakash Gupta
  • Louis H. Kauffman
  • Rama Mishra
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Abstract

Links in projective space ℝP3 can be represented by diagrams in ℝP2 where the projective plane ℝP2 is represented by a disk with antipodal identifications on the boundary. In this context if we place an n−strand braid β on this disk keeping its end points on the boundary then due to the identification of antipodal points it naturally represents a link diagram in ℝP3. We call this the projective closure of the braid β. In this paper we show that not all links in ℝP3 possess a diagram represented by projective closure of some braid.

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Cite

BibTeXRIS
BibTeX
@misc{gupta2026projective,
  title = {{Projective Braids in $\mathbbRP^3$}},
  author = {Aakash Gupta and Louis H. Kauffman and Rama Mishra},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.29058},
  eprint = {2609.29058},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.29058},
}
RIS
TY  - UNPB
TI  - Projective Braids in ℝP^3
AU  - Aakash Gupta
AU  - Louis H. Kauffman
AU  - Rama Mishra
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.29058
UR  - https://arxiv.org/abs/2609.29058
AB  - Links in projective space ℝP^3 can be represented by diagrams in ℝP^2 where the projective plane ℝP^2 is represented by a disk with antipodal identifications on the boundary. In this context if we place an n−strand braid β on this disk keeping its end points on the boundary then due to the identification of antipodal points it naturally represents a link diagram in ℝP^3. We call this the projective closure of the braid β. In this paper we show that not all links in ℝP^3 possess a diagram represented by projective closure of some braid.
ER  -