Semantic Scholar Open Access 2019 6 sitasi

Periodic projections of alternating knots

Antonio F. Costa Cam Van Quach-Hongler

Lihat Sumber DOI

Abstrak

In this paper we give a positive answer to a conjecture stated in by the authors in RACSAM 112(3) (2018), 793-802, by proving that: (1) any oriented prime alternating knot $K$ which is $q$-periodic, with $q\geq3$, has an alternating $q$-periodic projection. (2) if the prime alternating knot has no $q$-periodic alternating projection, the periodicity of $K$ is necessarily $q=2$. As applications we obtain the crossing number of a $q$-periodic alternating knot with $q\geq3$ is a multiple of $q$ and we give an elemantary proof that the knot $12a_{634}$ is not 3-periodic, our proof does not depends on computer as in "Periodic knots and Heegaard Floer correction terms" by Stanilav Jabuka and Swatee Naik (arXiv:1307.5116 [math.GT], to appear in the Journal of the European Mathematical Society).

Topik & Kata Kunci

Mathematics

Penulis (2)

Antonio F. Costa

Cam Van Quach-Hongler

Format Sitasi

APA MLA BibTeX

Costa, A.F., Quach-Hongler, C.V. (2019). Periodic projections of alternating knots. https://doi.org/10.1016/J.TOPOL.2021.107753

Akses Cepat

Lihat di Sumber doi.org/10.1016/J.TOPOL.2021.107753

Informasi Jurnal

Tahun Terbit: 2019
Bahasa: en
Total Sitasi: 6×
Sumber Database: Semantic Scholar
DOI: 10.1016/J.TOPOL.2021.107753
Akses: Open Access ✓