Raphael Appenzeller

activity

20242026

collaborators

7 papers

math.GT2026

Genus-zero links with prescribed knots as components

Raphael Appenzeller, José Pedro Quintanilha

We prove that any finite collection of at least three isotopy classes of knots in a 3-manifold $M$ is realizable as the components of a genus-zero link in $M$ , provided that an obv…

math.GT2026

All knots are trivial: a "proof" by sleight of hand

Raphael Appenzeller, José Pedro Quintanilha

We take a close look at a classical magic trick performed with a string, where a trivial knot is seemingly isotoped into a trefoil, and generalize it to a family of magic tricks fo…

math.GR2026

Semisimple algebraic groups over real closed fields

Raphael Appenzeller

We give a self-contained introduction to linear algebraic and semialgebraic groups over real closed fields, and we generalize several key results about semisimple Lie groups to alg…

math.GR2026

Generalized affine buildings for semisimple algebraic groups over real closed fields

Raphael Appenzeller

We use real algebraic geometry to construct an affine $Λ$ -building $B$ associated to the $F$ -points of a semisimple algebraic group, where $F$ is a valued real cl…

math.MG2025

Flat subsets of Euclidean buildings

Raphael Appenzeller, Auguste Hébert, Alexander Lytchak

We prove that any convex flat subset in a complete Euclidean building is contained in an apartment of the maximal system of apartments.

math.GR2025

Cops and robbers for hyperbolic and virtually free groups

Raphael Appenzeller, Kevin Klinge

Lee, Martínez-Pedroza and Rodríguez-Quinche define two new group invariants, the strong cop number $sCop$ and the weak cop number $wCop$ , by examining…

math.GR2024

Semialgebraic groups and generalized affine buildings

Raphael Appenzeller

We develop the theory of algebraic groups over real closed fields and apply the results to construct a geometric object $B$ and to prove that $B$ is an affine $…