Homepage of Benjamin Matthias Ruppik
Preprints
Resources
Activities
Summer Term 2020
Projects

Deeply slice knots
(joint with Michael Klug):
Knots in the boundary of a 4manifold W which bound a properly embedded
disk in W, but which are not nullconcordant in a collar neighborhood
\partial W x [0,1] of the boundary.
Deeply Slice Knots (.pdf, handwritten notes) 
FingerWhitney Unknotting Numbers
(joint with
Jason Joseph,
Michael Klug,
Hannah Schwartz):
Inspired by
SchneidermanTeichner's perspective on
Gabai's 4dimensional light bulb theorem
we define the
FingerWhitney unknotting number
of knotted 2spheres in S^4:
Since every 2knot 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_Wh(K)
as the minimal number of finger moves needed in such a process
to arrive at K.
We are trying to relate this to the 1handle stabilization
number and looked specifically at examples of ribbon
2knots and twistspins of classical knotted arcs.
FingerWhiteney Unknotting Numbers (.pdf, handwritten slides), FingerWhiteney Unknotting Numbers  Part 2 [Michael] (.pdf, handwritten slides)
Talks

IMPRS seminar at MPIM Bonn:
'Rasmussen's sinvariant and the local Thom conjecture' (.pdf, Handwritten Slides)
Conferences
 Topological Spring School, Matemale, October, 2020 (?)
Winter Term 2019/2020
 Milnor invariants study group  Part 2
Talks

Geometric Group Theory Study Group at MPIM Bonn:
Dehn Functions (.pdf, handwritten slides),
based on the book Office Hours with a Geometric Group Theorist (press.princeton.edu). 
IMPRS seminar at MPIM Bonn:
'Some faces of the Poincare homology sphere' (.pdf, Handwritten Notes),
Pictures and Links (.pdf, Slides).
Conferences
 Winter Braids X, Pisa, February 17  21, 2020
 Lowdimensional topology workshop, Regensburg, October 21  23, 2019.
Summer Term 2019
 Milnor invariants study group  Part 1

Poster for the BIGS exhibition in Bonn:
Ribbon concordances and doubly slice knots (.pdf)
Talks

IMPRS seminar at MPIM Bonn:
'Homology of the little disks operad' (.pdf, handwritten notes),
based on [Sinha] The homology of the little disks operad (arXiv:math/0610236). 
Research talk (on my master thesis)
'Stable classification of 4manifolds' (.pdf, handwritten notes) in the LKSSeminar (organized by Stefan Friedl and Clara Löh) at the university of Regensburg.
Conferences

Workshop on 4manifolds,
Bonn, September 16  20, 2019;
Slide for the picture show:
Resolving Ribbon Singularities (.pdf)
This is a picture of a standard construction which shows that every ribbon knot has a Seifert surface with an unlinked derivative. See [Cochran, Davis: Counterexamples to Kauffman's Conjectures on Slice Knots] (2014, arXiv:math/1303.4418) in the proof of Corollary 7.4.  Swiss Knots, Zurich, July 16  19, 2019.
 Knot concordance and lowdimensional manifolds, Le Croisic, June 17  21, 2019.

Knots and Braids in Norway,
Trondheim, May 2019;
Slides for the gong show talk:
Doubly Slice Knots (.pdf)
Winter Term 2018/2019

IMPRS welcome event, 10 minute talk:
'From knots to quantum invariants of 3manifolds' (.pdf, handwritten notes). 
Talk in the IMPRS seminar at MPIM Bonn:
'The trefoil and figureeight are not slice  An introduction to knot concordance' (.pdf, handwritten notes).
Summer Term 2018
 Material for the rep 'Introduction to Geometry and Topology' in the summer term 2018.
Winter Term 2017/2018
 An exercise (.pdf) where you use the LyndonHochschildSerre Spectral Sequence for a group extension to calculate the homology of the odd dihedral groups.

Study group on Kirby Calculus:
'Handle moves in Kirby Diagrams' (.pdf, handwritten notes)
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
 Project page for my bachelor thesis.