%0 Book Section
%T On the welded Tube map
%+ Institut de MathÃ©matiques de Marseille (I2M)
%A Audoux, Benjamin
%Z 23 pagesv2 : an error corrected and stylistic modifications
%Z I2M
%B Knot theory and its applications. ICTS program knot theory and its applications (KTH-2013), IISER Mohali, India, December 10--20, 2013
%8 2016
%D 2016
%Z 1408.5479
%R 10.1090/conm/670/13457
%K Tube map
%K welded knots
%K ribbon 2--knots
%Z Mathematics [math]/Geometric Topology [math.GT]Book sections
%X This note investigates the so-called Tube map which connects welded knots, that is a quotient of the virtual knot theory, to ribbon torus-knots, that is a restricted notion of fillable knotted tori in the 4-sphere. It emphasizes the fact that ribbon torus-knots with a given filling are in one-to-one correspondence with welded knots before quotient under classical Reidemeister moves and reformulates these moves and the known sources of non-injectivity of the Tube map in terms of filling changes.
%G English
%2 https://hal.archives-ouvertes.fr/hal-01066617/document
%2 https://hal.archives-ouvertes.fr/hal-01066617/file/OnTubeMap%20%281%29.pdf
%L hal-01066617
%U https://hal.archives-ouvertes.fr/hal-01066617
%~ CNRS
%~ EC-MARSEILLE
%~ INSMI
%~ I2M-2014-
%~ I2M
%~ UNIV-AMU
%~ TEST-AMU