Main menu: Home Research Teaching About Contact

Research Interests 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.

  1. Cubic graphs induced by bridge trisections [arXiv] with Abigail Thompson and Alexander Zupan
  2. Symplectic 4-manifolds admit Weinstein trisections [arXiv] with Peter Lambert-Cole and Laura Starkston
  3. Branched covers bounding rational homology balls [arXiv] with Paolo Aceto, Allison N. Miller, Maggie Miller, JungHwan Park, and András I. Stipsicz
  4. Note on 3-fold branched covers of S3 [arXiv] with Ryan Blair, Patricia Cahn, and Alexandra Kjuchukova
  5. Null, recursively starlike-equivalent sets shrink [arXiv] with Patrick Orson and Arunima Ray
  6. Generalized square knots and homotopy 4-spheres [arXiv] with Alexander Zupan
    To appear in Journal of Differential Geometry
  7. Bridge trisections in rational surfaces [arXiv] with Peter Lambert-Cole
    To appear in Journal of Topology and Analysis
  8. Doubly pointed trisection diagrams and surgery on 2-knots [arXiv] with David Gay
  9. Trisections and spun 4-manifolds [arXiv]
    Mathematical Research Letters 25(5) (2018), 1497 – 1524
  10. Bridge trisections of knotted surfaces in 4-manifolds [arXiv] with Alexander Zupan
    Proceedings of the National Academy of Sciences 115(43) (2018), 10880-10886
  11. Characterizing Dehn surgery on links via trisections [arXiv] with Alexander Zupan
    Procedings of the National Academy of Science 115(43) (2018), 10887-10893
  12. Bridge trisections of knotted surfaces in S4 [arXiv] with Alexander Zupan
    Transactions of the AMS, Vol. 369 (2017), 7343-7386
  13. Genus two trisections are standard [arXiv] with Alexander Zupan
    Geometry & Topology 21 (2017), 1583-1630
  14. A note on cabled slice knots and reducible surgeries [arXiv]
    Michigan Mathematics Journal Vol. 66, Issue 2 (2017), 269-276
  15. 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
  16. Doubly slice knots with low crossing number [arXiv] with Charles Livingston
    New York Journal of Mathematics, Vol. 21 (2015), 1007-1026
  17. Fibered ribbon disks [arXiv] with Kyle Larson
    Journal of Knot Theory and Its Ramifications, Vol. 24 (2015), 1550066, pp. 22
  18. Distinguishing topologically and smoothly doubly slice knots [arXiv]
    Journal of Topology 8 (2015), 315-351
  19. Small Seifert fibered surgery on hyperbolic pretzel knots [arXiv]
    Algebraic & Geometric Topology 14 (2014), 439-487
  20. 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.

Invited Talks

Below is a selection of invited talks I've given, along with links to some of the corresponding videos and slides.