Homepage of Benjamin Matthias Ruppik


Links to arXiv, ORCID, Google Scholar

Schematic of a regular homotopy

Casson-Whitney Unknotting Numbers of 2-spheres in the 4-sphere

Joint with Jason Joseph, Michael Klug, Hannah Schwartz: Inspired by Schneiderman-Teichner's perspective on Gabai's 4-dimensional light bulb theorem we define the Casson-Whitney unknotting number of knotted 2-spheres in S^4: Since every 2-knot K in S^4 can be obtained by first performing a number of (trivial) finger moves on the unknot, and in a next step removing the resulting intersection points in pairs via Whitney moves (along possibly complicated discs), we can define u_CW(K) as the minimal number of finger moves needed in such a process to arrive at K. We relate this to the 1-handle stabilization number and look specifically at examples of ribbon 2-knots and twist-spins of classical knotted arcs.
Finger-Whitney Unknotting Numbers - Part 1 (.pdf, handwritten slides), Finger-Whitney Unknotting Numbers - Part 2 [Michael] (.pdf, handwritten slides)

Homotopy classification of 4-manifolds with finite abelian 2-generator fundamental groups

[Daniel Kasprowski, Mark Powell, Benjamin Ruppik]
We show that for an oriented 4-dimensional Poincaré complex with finite fundamental group, whose 2-Sylow subgroup is abelian with at most 2 generators, the homotopy type is determined by its quadratic 2-type.




Winter Term 2020/2021

  • Topological Spring School, Matemale, October, 2020 (?)

Summer Term 2020


Winter Term 2019/2020

  • Winter Braids X, Pisa, February 17 - 21, 2020
  • Low-dimensional topology workshop, Regensburg, October 21 - 23, 2019.

Summer Term 2019


Winter Term 2018/2019

Summer Term 2018

  • Material for the rep 'Introduction to Geometry and Topology' in the summer term 2018.

Winter Term 2017/2018

Summer Term 2017

  • Material for the rep 'Introduction to Geometry and Topology' in the summer term 2017.
  • Handout (.pdf) for a talk on the First Lie Theorem.

Summer Term 2016


Links: Github, MathStackExchange