Daniel Müllner

I work as a software developer in Zürich, Switzerland. Before, I was postdoc in Gunnar Carlsson's group at Stanford University. Here are my contact details:

Address

Daniel Müllner
Funkwiesenstrasse 40
8050 Zürich
Switzerland
e-mail: 
public key

Research interests

Computational Topology, Topological Data Analysis

Teaching


Software


Hardware


Preprints


Publications


Dissertation: Orientation reversal of manifolds

Advisor: Prof. Matthias Kreck

I studied the phe­nome­non of chiral­ity in the con­text of mani­folds. A con­nected, orientable mani­fold is called amphi­cheiral if it admits an ori­en­ta­tion-​re­vers­ing self-​map and chiral if it does not. Many fa­mil­iar mani­folds like spheres or ori­entable sur­faces are amphi­cheiral: they can be embed­ded mirror-​sym­met­ri­cally into ℝn, as the fol­low­ing figure illus­trates.

2-sphereup-down-arrow
Reflect at the equator:
2-sphere with opposite orientation
torus
Similarly
up-down-arrow and up-down-arrow
surface of genus 2

On the other hand, exam­ples of chiral mani­folds have been known for many decades, e. g. the com­plex projec­tive spaces ℂP2k and some lens spaces in dimen­sions con­gruent 3 mod 4. A funda­mental ques­tion was in which dimen­sions chi­ral mani­folds exist. While every mani­fold in dimen­sions 1 and 2 is amphi­cheiral, one of my results is that in all other dimen­sions there exist chi­ral mani­folds.

For more information, read a summary or the dissertation itself: