In a classic paper Zeeman introduced the -twist spin of a knot and showed that the exterior of a twist spin fibers over . In particular this result shows that the knot is doubly slice. In this paper we give a quick proof of Zeeman’s result. The -twist spin of also gives rise to two metabolizers for and we determine these two metabolizers precisely.
Dans un article classique, Zeeman a introduit le -twist spin d’un nœud et montré que l’extérieur d’un twist spin fibre sur . En particulier ce résultat montre que le nœud est doublement concordant au nœud trivial. Dans cet article, nous donnons une démonstration rapide du résultat de Zeeman. Le -twist spin de produit deux métaboliseurs pour que nous déterminons précisément.
@article{AFST_2015_6_24_5_1203_0, author = {Stefan Friedl and Patrick Orson}, title = {Twist spinning of knots and metabolizers of {Blanchfield} pairings}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {1203--1218}, publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques}, address = {Toulouse}, volume = {Ser. 6, 24}, number = {5}, year = {2015}, doi = {10.5802/afst.1481}, zbl = {1348.57009}, language = {en}, url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1481/} }
TY - JOUR AU - Stefan Friedl AU - Patrick Orson TI - Twist spinning of knots and metabolizers of Blanchfield pairings JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2015 SP - 1203 EP - 1218 VL - 24 IS - 5 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1481/ DO - 10.5802/afst.1481 LA - en ID - AFST_2015_6_24_5_1203_0 ER -
%0 Journal Article %A Stefan Friedl %A Patrick Orson %T Twist spinning of knots and metabolizers of Blanchfield pairings %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2015 %P 1203-1218 %V 24 %N 5 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1481/ %R 10.5802/afst.1481 %G en %F AFST_2015_6_24_5_1203_0
Stefan Friedl; Patrick Orson. Twist spinning of knots and metabolizers of Blanchfield pairings. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 24 (2015) no. 5, pp. 1203-1218. doi : 10.5802/afst.1481. https://afst.centre-mersenne.org/articles/10.5802/afst.1481/
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