English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Unknotting numbers of 2-spheres in the 4-sphere

MPS-Authors
/persons/resource/persons267309

Joseph,  Jason M.
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons262013

Klug,  Michael R.
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons262559

Ruppik,  Benjamin M.
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons255515

Schwartz,  Hannah R.
Max Planck Institute for Mathematics, Max Planck Society;

External Resource
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)
There are no public fulltexts stored in PuRe
Supplementary Material (public)
There is no public supplementary material available
Citation

Joseph, J. M., Klug, M. R., Ruppik, B. M., & Schwartz, H. R. (2021). Unknotting numbers of 2-spheres in the 4-sphere. Journal of Topology, 14(4), 1321-1350. doi:10.1112/topo.12209.


Cite as: https://hdl.handle.net/21.11116/0000-0009-79C6-0
Abstract
We compare two naturally arising notions of unknotting number for 2-spheres
in the 4-sphere: namely, the minimal number of 1-handle stabilizations needed
to obtain an unknotted surface, and the minimal number of Whitney moves
required in a regular homotopy to the unknotted 2-sphere. We refer to these
invariants as the stabilization number and the Casson-Whitney number of the
sphere, respectively. Using both algebraic and geometric techniques, we show
that the stabilization number is bounded above by one more than the
Casson-Whitney number. We also provide explicit families of spheres for which
these invariants are equal, as well as families for which they are distinct.
Furthermore, we give additional bounds for both invariants, concrete examples
of their non-additivity, and applications to classical unknotting number of
1-knots.