|
|
Juniorprofessor
Fachbereich Mathematik
Schwerpunkt Algebra und Zahlentheorie
Bundesstraße 55 (Geomatikum)
20146 Hamburg
Raum 334
Tel.: +49 40 42838-5194
Fax: +49 40 42838-5190
E-Mail:
christoph (at) wockel.eu
Office hour:
Wed. 13-14 and on appointment
|
|
My current research concerns the occurrence of infinite-dimensional Lie groups in higher bundle- and gauge
theory. In particular, I am interested in understanding different models for the string group by methods from
infinite-dimensional Lie theory and on overcoming obstructions for Lie theoretic integration procedures by
passing from Lie groups to Lie 2-groups or group stacks. This comprises
- dissolving obstructions for integrating central extensions of infinite-dimensional Lie groups by
group stacks
- integrating central extensions of Lie 2-algebras
- the relationship between differentiable and locally smooth group cohomology
- higher connected covers of topological groups with a perspective to string group models
- string bundles as principal 2-bundles
-
Non-integral central extensions of loop groups,
12 pp., to appear in Contemp. Math.
(arXiv-version)
-
Principal 2-bundles and their gauge 2-groups,
40 pp., to appear in Forum Math.
(arXiv-version)
-
Central Extensions of Groups of Section
(with Karl-Hermann Neeb),
Ann. Glob. Anal. Geom., to appear
(arXiv-version)
-
Equivalences of Smooth and Continuous Principal
Bundles with
Infinite-Dimensional Structure Group
(with Christoph Müller), Adv. Geom., 9 (4) (2009) 605-626
(arXiv-version)
-
A Generalisation of Steenrod's Approximation
Theorem,
Arch.
Math. (Brno) 45 (2009) 95-104
(arXiv-version)
-
Lie Group Structures on Symmetry Groups of Principal
Bundles,
J. Funct. Anal. 251 (2007) 254-288
(arXiv-version)
- The Samelson Product and Rational Homotopy
for Gauge Groups,
Abh. Math. Sem. Univ. Hamburg 77 (2007) 219-228
(arXiv-version)
- Smooth Extensions and Spaces of Smooth and
Holomorphic Mappings, J. Geom. Symmetry Phys.,
5 (2006) 118-126 (arXiv-version)
Preprints:
- 24.05.2009, Higher connected covers by categorified principal bundles, Workshop on Topological Field Theories, (Northwestern University, USA), Extended notes by Alex Hoffnung
- 08.04.2009, Non-integral central extensions of loop groups via gerbes, Workshop on Homotopy Theory of Function Spaces and Related Topics, (Oberwolfach, Germany)
- 16.1.2009, Categorical Lie groups and Lie's Third Theorem for locally
exponential Lie algebras,
Seminar Sophus Lie 2009 (Paderborn, Germany)
- 30.9.2008, Universal group cocycles for simplicial groups,
Buildings 2008, (Münster, Germany),
- 19.05.2008, Gauge groups for lifting gerbes and principal
2-bundles,
University of Paderborn (Germany), invited by Helge
Glöckner,
slides
- 22.01.2008, Erweiterungstheorie von
Eichtransformationsgruppen,
Humbold Universität Berlin (Germany), invited by Ilka
Agricola
- 31.05.2007, A bundle-theoretic perspective
to Kac-Moody groups and their generalisations,
Colloquium of the
Graduiertenkolleg
Gruppen und Geometrie, (Göttingen, Germany)
slides
- 29.01.2007, A bundle-theoretic perspective
to Kac-Moody groups and their generalisations,
University of Münster (Germany), invited by Linus Kramer
- 02.11.2006, Approximation Theorems for Locally Convex
Manifolds, Lie Groups and Principal Bundles,
Seminar Sophus Lie 2006 (Vienna, Austria)
slides
- 16.06.2006, Equivalences of continuous and smooth principal
bundles, 31. Süddeutsches Kolloquium
über Differentialgeometrie (Darmstadt, Germany),
slides
(in German)
- 12.05.2006, Topological properties of Gauge Groups and
Applications to thier Infinite-Dimensional Lie Theory,
Colloquium of the
Graduiertenkolleg
Gruppen und Geometrie, (Göttingen, Germany)
- 29.06.2005, Infinte-dimensional Lie theory for Gauge
Groups,
Workshop "Geometric
Methods in Physics" (Bialowieza, Poland),
abstract
,
slides
- 11.06.2005, Infinte-dimensional Lie Theory for Gauge
Groups,
Seminar Sophus Lie 2005 (Nancy, France),
abstract,
slides
- 15.09.2004, Zentrale Erweiterungen von Eichgruppen,
DMV-Jahrestagung 2004 (Heidelberg, Germany),
slides
- 15.11.2003, Zentrale Erweiterungen von Eichgruppen,
Workshop "Infinite-dimensional Lie theory"
(Darmstadt, Germany)
|
|