Duncan McCoy

Email: mc_coy dot duncan at uqam dot caOffice: PK-5320
Postal address:Département de mathématiques,Université du Québec à Montréal,PO Box 8888, centre-ville,Montréal H3C 3P8,Québec, Canada

Duncan McCoy

I am an assistant professor of mathematics at l'Université du Québec à Montréal, where I hold a Canada Research Chair in low-dimensional topology. My research is concentrated on 3-manifolds, 4-manifolds and their applications to knot theory.

Previously, I was a Bing Postdoctoral Fellow at the University of Texas at Austin and I completed my PhD at the University of Glasgow in 2016. You can explore my full mathematical lineage here. My thesis is available from the arXiv and the University of Glasgow's repository.

You may also appreciate some unreasonably amusing number theory.

Preprints:

Cusp types of arithmetic hyperbolic manifolds
-with Connor Sell - arXiv
The search for alternating surgeries
- with Ken Baker & Marc Kegel - arXiv
Quasi-alternating surgeries
- with Ken Baker & Marc Kegel - arXiv
A survey on embeddings of 3-manifolds in definite 4-manifolds
- with Paolo Aceto & JungHwan Park - accepted Proceedings of MSJ-KMS Joint Meeting 2023 - arXiv

Publications:

Definite fillings of lens spaces
- with Paolo Aceto & JungHwan Park - J. Differential Geom. 131(1): 1-41 (2025) - arXiv
Two curious strongly invertible L-space knots
- with Ken Baker & Marc Kegel - Adv. Math. 403 (2025), 110287- arXiv
Non-integer characterizing slopes and knot Floer homology
- Int. Math. Res. Not. IMRN 2025-5, rnaf043, (2025) - arXiv
Doubly slice Montesinos links
- with Clayton McDonald - Michigan Math. J. 74 (1), (2024), 85-117 - arXiv
Characterizing slopes for the (-2,3,7)-pretzel knot

-Canad. Math. Bull. 66-3 (2023), 937-950 - arXiv

The realization problem for non-integer Seifert fibered surgeries
- with Ahmad Issa - Algebr. Geom. Topol. 23-4 (2023), 1501-1550- arXiv
The Montesinos trick for proper rational tangle replacement
- with Raphael Zentner - Proc. Amer. Math. Soc. 151 (2023), no. 4, 1811–1822 - arXiv
Non-simply connected symplectic fillings of lens spaces
- with Paolo Aceto & JungHwan Park - Bull. London Math. Soc. 54-3 (2022), 1010--1026 - arXiv
Surgeries, sharp 4-manifolds and the Alexander polynomial
- Algebr. Geom. Topol. 21-5 (2021), 2649--2676 - arXiv
Null-homologous twisting and the algebraic genus
- 2019–20 MATRIX annals, 147--165, Springer 2021 - arXiv
Gaps between consecutive untwisting numbers
- Glasgow. Math. J. 63 (2021), no. 1, 59-67 - arXiv
Non-integer characterizing slopes for torus knots
- Comm. Anal. Geom. 28 (2020), no. 7, 1647-1682- arXiv
Smoothly embedding Seifert fibered spaces in S^4
- with Ahmad Issa -Trans. Amer. Math. Soc. 373 (2020), no. 7, 4933–4974 - arXiv
On Seifert fibered spaces bounding definite manifolds
- with Ahmad Issa - Pacific J. Math. 304 (2020), No. 2, 463–480 - arXiv
On the characterising slopes of hyperbolic knots
- Math. Res. Let. 26 (2019), no. 5, 1517-1526 - arXiv
On L-space knots obtained from unknotting arcs in alternating diagrams
- with Andrew Donald & Faramarz Vafaee - New York J. Math. 25 (2019), 518–540 - arXiv
On calculating the slice genera of 11- and 12-crossing knots
- with Lukas Lewark - Exp. Math. 28 (2019), no. 1, 81–94 - arXiv
Bounds on alternating surgery slopes
- Algebr. Geom. Topol. 17 (2017), no. 5, 2603–2634 - arXiv
Alternating knots with unknotting number one
- Adv. Math. 305 (2017), 757–802 - arXiv
On 2-bridge knots with differing smooth and topological slice genera
- with Peter Feller - Proc. Amer. Math. Soc. 144 (2016), no. 12, 5435–5442 - arXiv
Non-integer surgery and branched double covers of alternating knots
- J. Lond. Math. Soc. (2) 92 (2015), no. 2, 311–337 - arXiv

Other things:

The Small Seifert Fibred Embeddahedron
-with Ahmad Issa - Mathematical Research Postcards - link

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