Strings, operads and Morse homology

PhD defence by Jonathan Laurent Clivio

Assessment Committee

Professor Jesper Grodal, Mathematics, University of Copenhagen (Chairperson)
Professor Alexandru Oancea, University of Strasbourg
Tenured Assistant Professor Florian Naef, Trinity College Dublin

Supervisors

Professor Nathalie Anne-Marie Thierry Wahl

Department

Department of Mathematical Sciences

Place

The defence is conducted as a hybrid defence.

To attend the defence in person:
Building: Niels Bohr building, Room: Margrethe Bohr auditorium,
Jagtvej 155, 2200 Copenhagen N

To attend the defence online:
Please follow the link to attend the defence online: https://ucph-ku.zoom.us/j/69505768966?pwd=mYfJI4lOWPuwWag8EgwlG58b3yAuu0.1
MeetingID, if relevant: 695 0576 8966
Password, if relevant: 684247

Email address to gain access to the thesis: jonathan.clivio@hispeed.ch.
You will either receive a copy of the thesis or be informed where you can read a physical copy.
Recipients of copies of the thesis are not allowed to share or distribute it due to copyright compliance.

Short description of the thesis

This thesis is a synopsis consisting of three articles that study different aspects of string topology– an area of research intersecting geometry and topology. The first article studies graded Frobenius algebras. They are an algebraic structure that appears in, but not only in, string topology. We give an algebraic gadget, a PROP, that encodes and explains this algebraic structure. The second article studies the string topology coproduct on the subspace of based loop. We prove that the coproduct is better behaved on this subspace. We use this understanding to give explicit computations for certain manifolds. The third and final article of this synopsis studies the string topology coproduct via Morse homology with differential graded coefficients. Using this Morse theoretic framework, we reconstruct the coproduct on the free loop space from the coproduct on the based loop space.