Daniel Müllner

I was a postdoc in Gunnar Carlsson's group at Stanford University until 8/2013. Here are my new contact details:

Address

Daniel Müllner
Tobelsteig 3
8046 Zürich
Switzerland
e-mail: emil
public key

Research interests

Computational Topology, Topological Data Analysis

Teaching


Software


Preprints


Publications


Dissertation: Orientation reversal of manifolds

Advisor: Prof. Matthias Kreck

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

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: