Brendan Owens

Professor of Mathematics, Adviser of Studies, Head of Mathematics

Room 434 Mathematics and Statistics Building
School of Mathematics and Statistics
University of Glasgow

Brendan [dot] Owens [at] glasgow [dot] ac [dot] uk

Research

My research is in low-dimensional topology. I am interested in smooth 3-manifolds, 4-manifolds and knots, and in the use of gauge-theoretic invariants of manifolds, especially Floer homology groups.

Mathematical genealogy.

Papers

You can also find my papers on the arXiv, on MathSciNet, and on zbMATH.

• (with J. Greene) Alternating links, rational balls, and cube tilings, arXiv:2212.06248, accepted for publication in J. Eur. Math. Soc.
• (with S. Strle) Disoriented homology and double branched covers, arXiv:2207.09358, Canad. J. Math. 76 (2024), no. 3, 731--773.
• (with F. Swenton) An algorithm to find ribbon disks for alternating knots, arXiv:2102.11778, Exp. Math. 33 (2023), no. 3, 437--455.
• Smooth, nonsymplectic embeddings of rational balls in the complex projective plane, Q. J. Math. 71 (2020), no. 3, 997--1007.
• Knots and 4-manifolds, Winter Braids Lect. Notes 6 (2019), no. IX, Exp. No. II, 26 pp.
• Equivariant embeddings of rational homology balls, Q. J. Math. 69 (2018), no. 3, 1101--1121.
• (with S. Strle) Immersed disks, slicing numbers and concordance unknotting numbers, Comm. Anal. Geom. 24 (2016), no. 5, 1107--1138.
• (with M. Nagel) Unlinking information from 4-manifolds, Bull. London Math. Soc. 47 (2015), no. 6, 964--979.
• (with P. Lisca) Signatures, Heegaard Floer correction terms and quasi-alternating links, Proc. Amer. Math. Soc. 143 (2015), no. 2, 907--914.
• (with R. Bieri and P. Kropholler) On subsets of Sⁿ whose (n+1)-point subsets are contained in open hemispheres, New York J. Math. 20 (2014), 1021--1041.
• (with A. Donald) Concordance groups of links, Algebr. Geom. Topol. 12 (2012), no. 4, 2069--2093.
• (with S. Strle) Dehn surgeries and negative-definite four-manifolds, Selecta Math. (N.S.) 18 (2012), no. 4, 839--854.
• (with S. Strle) A characterisation of the Zⁿ⊕ Z(δ) lattice and definite nonunimodular intersection forms, Amer. J. Math. 134 (2012), no. 4, 891--913.
• On slicing invariants of knots, Trans. Amer. Math. Soc. 362 (2010), no. 6, 3095--3106.
• Unknotting information from Heegaard Floer homology, Adv. Math. 217 (2008), no. 5, 2353--2376.
• (with C. Manolescu) A concordance invariant from the Floer homology of double branched covers, Int. Math. Res. Not. IMRN 2007, no. 20, Art. ID rnm077, 21 pp.
• (with S. Strle) A characterisation of the n⟨1⟩⊕⟨3⟩ form and applications to rational homology spheres, Math. Res. Lett. 13 (2006), no. 2, 259--271.
• (with S. Strle) Rational homology spheres and the four-ball genus of knots, Adv. Math. 200 (2006), no. 1, 196--216.
• (with S. Strle) Definite manifolds bounded by rational homology three spheres, ``Geometry and Topology of Manifolds'', Fields Institute Communications, Vol. 47, AMS (2005), pages 243--252.
• Instantons on cylindrical manifolds and stable bundles, Geometry and Topology, Vol. 5 (2001) Paper no. 24, pages 761--797.

PhD students

Please get in touch if you are interested in doing a PhD under my supervision.

Former students and their theses

• Andrew Donald (2013), Embedding 3-manifolds in 4-space and link concordance via double branched covers.
• Duncan McCoy (2016), Alternating surgeries.
• Daniel Waite (2020), Three-strand pretzel knots, knot Floer homology and concordance invariants.
• Vitalijs Brejevs (joint with Andy Wand, 2022), On slice alternating 3-braid closures and Stein-fillable genus one open books.
• Tanushree Shah (joint with Ana Lecuona and Andy Wand, 2023), Classification of tight contact structures on some Seifert fibred manifolds with four exceptional fibres.
• Weizhe Niu (joint with Mark Powell, 2024), Mapping class groups of 4-manifolds via barbell diffeomorphisms, Budney-Gabai invariants and handle structures.

Current students

Giulia Carfora, Simeon Hellsten.

Teaching

2023-24

• Maths 2F (semester 2). Course Moodle page.

Links

• Glasgow Geometry and Topology group.
• Glasgow Geometry and Topology seminar.
• Core Structures @ Glasgow.
• Scottish Topology Seminar.
• I am on the editorial board of the Journal and Bulletin of the LMS.
• ICERM workshop: Links in dimensions 3 and 4 (Providence, Rhode Island, 12--16 May, 2025).

Computer programs

• A maple program for computing the d-invariants of a positive semi-definite symmetric matrix. (Written jointly with S. Strle.)
• Mathematica programs to compute the Goeritz matrices of a link, and also to compute signature and nullity of a symmetric matrix, or of a link.
• A maple program for computing the Levine-Tristram signature function of a torus knot (based on Litherland's paper).

About this page

Page design by Patrick Ingram, via Liam Watson.

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