Allison H. Moore

Research

My research is in low-dimensional topology and geometry, especially invariants of knots and links in three and four-manifolds. I often use Heegaard Floer homology or Khovanov homology, and many of my results involve local operations on knots like crossing changes, band surgeries and mutations. I have a secondary research interest in the applications of topology to physical systems, for example, how to model and characterize enzymatic actions on circular DNA molecules.

mutation surface pretzel kauffman states

Here is a link to my papers on the arXiv. Authorship on all articles is alphabetical.

Acknowledgements: My work has been previously supported by the National Science Foundation and is currently supported by the The Thomas F. and Kate Miller Jeffress Memorial Trust, Bank of America, Trustee.

Preprints

Artem Kotelskiy, Tye Lidman, Allison H. Moore, Liam Watson, Claudius Zibrowius. Cosmetic operations and Khovanov multicurves. arXiv:2109.14049 [math.GT], Submitted 2021.
arXiv, PDF

Kenneth L. Baker, Dorothy Buck, Danielle O'Donnol, Allison H. Moore, Scott Taylor. Primality of theta-curves with proper rational tangle unknotting number one. arXiv:2201.08213 [math.GT], 2022.
arXiv, PDF

Publications / Accepted

Eugene Gorsky, Beibei Liu, Tye Lidman and Allison H. Moore. Heegaard Floer homology and triple linking. arXiv:2006.15484 [math.GT], 2020. Accepted at International Mathematical Research Notices.
arXiv, PDF

Tye Lidman, Allison H. Moore and Claudius Zibrowius. L-space knots have no essential Conway spheres. arXiv:2006.03521 [math.GT], 2021. To appear in Geometry & Topology.
arXiv, PDF

Stanislav Jabuka, Beibei Liu, and Allison H. Moore. Knot graphs and Gromov hyperbolicity. arXiv:1912.03766 [math.GT], 2020. Accepted at Mathematische Zeitschrift.
arXiv, PDF

Christopher Flippen, Allison H. Moore, and Essak Seddiq. Quotients of the Gordian and H(2)-Gordian graphs. Journal of Knot Theory and Its Ramifications 30 (2021), no. 5, Paper No. 2150037, 23 pp.
JKTR, arXiv, PDF

Allison H. Moore and Mariel Vazquez. A note on band surgery and the signature of a knot. Bulletin of the London Mathematical Society, 52(6):1191--1208, 2020.
BLMS, arXiv, PDF

Eugene Gorsky, Beibei Liu and Allison H. Moore. Surgery on links of linking number zero and the Heegaard Floer d-invariant. Quantum Topology 11(2):323--378, 2020.
Quantum Topology, arXiv, PDF

Allison H. Moore and Mariel H. Vazquez. Recent advances on the non-coherent band surgery model for site-specific recombination. In Topology and geometry of biopolymers, volume 746 of Contemporary Mathematics, pages 101–125. Amer. Math. Soc., Providence, RI, 2020.
Contemporary Math, arXiv, PDF

Tye Lidman, Allison H. Moore and Mariel Vazquez. Distance one lens space fillings and band surgeries. Algebraic & Geometric Topology; 19(5):2439--2484, 2019.
AGT, arXiv, PDF.

Kenneth L. Baker and Allison H. Moore. Montesinos knots, Hopf plumbings, and L-space surgeries. Journal of the Mathematical Society of Japan, 70(1):95--110, 2018.
J. Math Japan, arXiv, PDF

Tye Lidman and Allison H. Moore. Cosmetic surgery in L-spaces and nugatory crossings. Transactions of the American Mathematical Society, 369(5):3639--3654, 2017.
Transactions, arXiv, PDF.

Tye Lidman and Allison H. Moore. Pretzel knots with L-space surgeries. Michigan Mathematical Journal, 65(1):105–130, 2016.
Michigan, arXiv, PDF

Allison H. Moore. Symmetric unions without cosmetic crossing changes. Advances in the Mathematical Sciences: Research from the 2015 Association for Women in Mathematics Symposium, volume 6, pages 103–116. Springer International Publishing, Cham, 2016.
Advances, arXiv, PDF

Allison H. Moore and Laura Starkston. Genus-two mutant knots with the same dimension in knot Floer and Khovanov homologies. Algebraic & Geometric Topology, 15(1):43–63, 2015.
AGT, arXiv, PDF

Thesis

Allison H. Moore. Behavior of knot Floer homology under Conway and genus two mutation. PhD Dissertation, The University of Texas at Austin, May 2013.
Dissertation repository

Software

Braid Generator: Software to generate random braid representatives of a fixed knot type via Markov chain
M. Nasrollahi, S. Witte and A. H. Moore, June 2019
Project now publicly available on Github! and at PyPi.org.

Undergraduate Researchers

Research opportunities for undergrads in Fall 2021 -- Summer 2022

Project description:

Knots and links are embeddings of closed loops in three-dimensional space. Knot and link invariants are mathematical objects that capture topological and geometric information about the link and its three-dimensional complement. This project seeks to advance our mathematical understanding of basic operations on knots and links, to explore the relationships between invariants of knots and three-manifolds, and to leverage these developments toward knot-theoretic models of DNA recombination mediated by enzymes. The central hypothesis of the proposal is that knot theory provides a rigorous mathematical framework with which to investigate molecular knotting and entanglement in DNA.

Students with a genuine interest in topology and geometry or some background in linear algebra or coding will be most successful. Prior knowledge of knot theory is not required, and essential skills can be learned along the way. There are some funds to pay students an hourly wage. Students from underrepresented groups are especially encouraged to apply.

Any VCU undergrads or grad students who are curious about this research project, a summer project, or interested in independent study, please get in touch with me by email (moorea14 at VCU dot edu).

Past student projects:

I've had the privilege of working with many excellent undergraduate researchers. Here is a subset of them (and do please contact me if you don't see your name here and would like a shout-out!):

  • Essak Seddiq and Christopher Flippen, VCU, 2020. Quotients of the Gordian graph of knots. Link to our arXiv preprint. (To appear in the Journal of Knot Theory and its Ramifications).
  • Milad Nasrollahi, UC Davis, 2019. BraidGenerator: Software using a Markov chain algorithm to generate random braids of fixed knot type. (Available at GitHub and PyPi).
  • Phoebe Song, UC Davis, 2019. The Jones polynomial mod p.
  • Kaidi Shao, UC Davis, 2018. Neural Nets and Knot Invariants (project with S. Witte)
  • Chris Harshaw, Victor Prieto and Konstantinos Varvarezos, Rice University, 2016.
    Paper: On the Number of Equivalence Classes of p-Colorings of Symmetric Unions.
  • Topological Molecular Biology at UC Davis

    At UC Davis, I held a joint appointment in the Topological Molecular Biology lab, in the department of microbiology and molecular genetics. Part of my research at UC Davis was funded by the NSF, with PI M. Vazquez.

    nugatory crossing reconnection