Dirk Schütz's Homepage

Research

My research interests include

Knot Theory
Topological Robotics
Topology of closed 1-forms
Assembly maps in algebraic K- and L-theory
Parametrized fixed point theory

For more information on research in topology here in Durham see the Durham Pure Mathematics Research Page.

The 2020 British Topology Meeting took place 12-14 April 2022.

The Durham Conference on Geometry and Topology in Honour of John Bolton and Cherry Kearton took place 20-22 June 2010.

Teaching

Office hours : TBA.

Michaelmas Term 2024:

Analysis I.
MAGIC course Differential topology and Morse theory.

Previous Terms.

Recent Publications and Preprints

Preprints:

On variations of s-invariants from sl₃-link homology, preprint. pdf.
On the Khovanov homology of 3-braids, preprint. pdf.
Local equivalence and refinements of Rasmussen's s-invariant, preprint, with N. Dunfield and R. Lipshitz. pdf.
Two second Steenrod squares for odd Khovanov homology, preprint. pdf.

Recent Publications:

A note on the X-torsion order of a knot, preprint, to appear in Canad. Math. Bull. The original publication is available here. pdf.
On an integral version of the Rasmussen invariant, Michigan Math. J. 75 (2025), 65-88. The original publication is available here. pdf.
A calculus for flow categories, with A. Lobb and P. Orson, Adv. Math. 409 B (2022), 108665, 58pp. The original publication is available here. pdf.
A scanning algorithm for odd Khovanov homology, Algebr. Geom. Topol. 22 (2022), 1287-1324. The original publication is available here. pdf. Additional material.
A fast algorithm for calculating s-invariants, Glasg. Math. J. 63 (2021), 378-399. The original publication is available here and a corrigendum here. pdf. Additional material.
Arbitrarily large torsion in Khovanov cohomology, with S. Mukherjee, Quantum Top. 12 (2021), 243-264. The original publication is available here. pdf.
Torsion calculations in Khovanov cohomology, J. Knot Theory Ramifications 29 (2020), 2071001, 7pp. The original publication is available here. pdf. Additional material.
Khovanov homotopy calculations using flow category calculus, with A. Lobb and P. Orson, Exp. Math. 29 (2020), 475-500. The original publication is available here. pdf. Additional material.
An sl_n stable homotopy type for matched diagrams, with D. Jones and A. Lobb, Adv. Math. 356 (2019), 106816, 70pp. The original publication is available here. pdf. Additional material.
Framed cobordism and flow category moves, with A. Lobb and P. Orson, Algebr. Geom. Topol. 18 (2018), 2821-2858. The original publication is available here. pdf.
Morse moves in flow categories, with D. Jones and A. Lobb, Indiana Univ. Math. J. 66 (2017), 1603-1657. The original publication is available here. pdf.
A Khovanov stable homotopy type for colored links, with A. Lobb and P. Orson, Algebr. Geom. Topol. 17 (2017), 1261-1281. The original publication is available here. pdf. Additional material.

A full list of publications is available here.

Software

Here is some software that I have written over the years.

KnotJob. A programme calculating various knot invariants.

last modified: 11.04.2025.