2017/02/28 by Yuta Nozaki · 3 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #Alexander polynomial #Biology #Botany #Connective tissue disorders research #Fibered knot #Genus #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Knot (papermaking) #Knot theory #Lens (geology) #Lens space #Mathematics #Paleontology #Pure mathematics #math.GT #math.NT #msc:11R45 #msc:57M27
paper · pdf · doi:10.1215/ijm/1552442658
published in Illinois Journal of Mathematics 62(1-4) (Duke University Press) · 13 pages, 3 figures
openalex publication_date 2018/01/01 · arxiv created 2019/01/17 · arxiv updated 2019/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove that every lens space contains a genus one homologically fibered knot, which is contrast to the fact that some lens spaces contain no genus one fibered knot. In the proof, the Chebotarev density theorem and binary quadratic forms in number theory play a key role. We also discuss the Alexander polynomial of homologically fibered knots.