Research Jeffrey Meier
Broadly, I am interested in knot theory, knotted surfaces, and the topology of 3-manifolds and 4-manifolds. In particular, I have a great interest in trisections of 4-manifolds; 4-dimensional knot theory, including fibered ribbon 2-knots, knotted Klein bottles and projective planes, surgery operations, and bridge trisections; various aspects of knot concordance, including doubly slice knots, fibered ribbon knots, cabled slice knots, and applications of knot homology theories; and Dehn surgery, especially exceptional surgery and Seifert fibered surgery.
- Positive braids minimize ascending number [arXiv] with Lowell Davis
Roller-coaster algorithm SnapPy code (.ipynb)
Submitted - Ribbon numbers for 12-crossing knots [arXiv] with Evan Scott, Alexander Zupan et. Al.
Submitted - Knots with non-isotopic ribbon disks [arXiv] with Alexander Zupan
Submitted - Bridge trisections and Seifert solids [arXiv] with Jason Joseph, Maggie Miller, and Alexander Zupan
To appear in Pacific Journal of Mathematics - Toric multisections and curves in rational surfaces [arXiv] with Gabriel Islambouli, Homayun Karimi, and Peter Lambert-Cole
Journal of Topology and Analysis 14 (2022), no. 3, 655-708 - Bridge trisections and classical knotted surface theory [arXiv] with Jason Joseph, Maggie Miller, and Alexander Zupan
Pacific Journal of Mathematics 319 (2022), no. 2, 343–369 - Filling braided links with trisected surfaces [arXiv]
Algebraic & Geometric Topology 24 (2024), no. 2, 803–895 - Cubic graphs induced by bridge trisections [arXiv] with Abigail Thompson and Alexander Zupan
Mathematical Research Letters 30 (2023), no. 4, 1207–1231 - Symplectic 4-manifolds admit Weinstein trisections [arXiv] with Peter Lambert-Cole and Laura Starkston
Journal of Topology 14(2) (2021), 641–673 - Branched covers bounding rational homology balls [arXiv] with Paolo Aceto, Allison N. Miller, Maggie Miller, JungHwan Park, and András I. Stipsicz
Algebraic & Geometric Topology 21 (2021) 3569–3599 - Note on 3-fold branched covers of S3 [arXiv] with Ryan Blair, Patricia Cahn, and Alexandra Kjuchukova
Annales de l’Institute Fourier (Grenoble) 74 (2024), no. 2, 849–866 - Null, recursively starlike-equivalent sets shrink [arXiv] with Patrick Orson and Arunima Ray
Glasgow Mathematical Journal 65 (2023), no. 2, 328-336 - Generalized square knots and homotopy 4-spheres [arXiv] with Alexander Zupan
Journal of Differential Geometry 122(1): 69-129 (2022) - Bridge trisections in rational surfaces [arXiv] with Peter Lambert-Cole
Journal of Topology and Analysis 14 (2022), no. 3, 655-708 - Doubly pointed trisection diagrams and surgery on 2-knots [arXiv] with David Gay
Mathemathtical Proceedings of the Cambridge Philosophical Society 172(1) (2022), 163-195 - Shrinking starlike sets with Patrick Orson and Arunima Ray
in The 4-dimensional Disc Embedding Theorem (based on lectures by Michael H. Freedman) edited by Stefan Behrens, Boldizsár Kalmár, Min Hoon Kim, Mark Powell, and Arunima Ray Oxford University Press, Oxford, 2021. xvii+473 pp. ISBN:978-0-19-884131-9 - Trisections and spun 4-manifolds [arXiv]
Mathematical Research Letters 25(5) (2018), 1497–1524 - Bridge trisections of knotted surfaces in 4-manifolds [arXiv] with Alexander Zupan
Proceedings of the National Academy of Sciences 115(43) (2018), 10880-10886 - Characterizing Dehn surgery on links via trisections [arXiv] with Alexander Zupan
Procedings of the National Academy of Science 115(43) (2018), 10887-10893 - Bridge trisections of knotted surfaces in S4 [arXiv] with Alexander Zupan
Transactions of the AMS, Vol. 369 (2017), 7343-7386 - Genus two trisections are standard [arXiv] with Alexander Zupan
Geometry & Topology 21 (2017), 1583-1630 - A note on cabled slice knots and reducible surgeries [arXiv]
Michigan Mathematics Journal Vol. 66, Issue 2 (2017), 269-276 - Classifying trisections and the Generalized Property R Conjecture [arXiv] with Alexander Zupan and Trenton Schirmer
Proceedings of the AMS, Vol. 144(11) (2016), 4983-4997 - Doubly slice knots with low crossing number [arXiv] with Charles Livingston
New York Journal of Mathematics, Vol. 21 (2015), 1007-1026 - Fibered ribbon disks [arXiv] with Kyle Larson
Journal of Knot Theory and Its Ramifications, Vol. 24 (2015), 1550066, pp. 22 - Distinguishing topologically and smoothly doubly slice knots [arXiv]
Journal of Topology 8 (2015), 315-351 - Small Seifert fibered surgery on hyperbolic pretzel knots [arXiv]
Algebraic & Geometric Topology 14 (2014), 439-487 - Isolation-by-distance and outbreeding depression are sufficient to drive parapatric speciation in the absence of environmental influences with René Doursat, Rich Drewes, and Guy Hoelzer
PLoS Computational Biology 4(7) (2008), 11 pp.
Videos and Slides
Here are some videos and slides from talks I've given.- Classifying fibered, homotopy-ribbon disks [Google Drive]
- Cataloging knotted surfaces [Google Drive]
- Trisections and homotopy four-spheres [Dropbox]
- Tangles, 2-knots, and Trisections [Slides]
- Bridge trisections of surfaces in four-manifolds [Video (courtesy of CIRM)]
- Bridge trisections for knotted surfaces in the 4-sphere [Video (courtesy of BIRS), Slides]
- Trisecting the Gluck twist [Slides]
- Fibered Ribbon Disks [Slides]
- Seifert Fibered Surgery on Hyperbolic Montesinos Knots [Google Drive]
- Knots, Seifert Surfaces, and the Slice-Ribbon Conjecture [Video (courtesy of the UT Austin Math Club)]