ERC grant OXTOP

Low-dimensional topology in Oxford

University of Oxford

This project aims to build a group that brings together experts in gauge-theoretic, geometric, and group-theoretic techniques. It consists of 4 main branches:

Cobordism maps in knot Floer homology

TQFTs

Heegaard Floer homology and geometric structures

The Fox conjecture

Principal Investigator:

Postdoctoral researchers:

PhDs:

Former members:

Publications supported by the grant:

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  Handle decompositions of rational balls and Casson–Gordon invariants
  P. Aceto, M. Golla, and A. Lecuona, Proc. Amer. Maths. Soc. 146 (9), 4059 - 4072 (2018).
  • ArXiv version
  The Reidemeister graph is a complete knot invariant
  A. Barbensi and D. Celoria, preprint (2018).
  • ArXiv version
  On concordances in 3-manifolds
  D. Celoria, J. Topol. 11 (1), 180 - 200 (2018).
  • ArXiv version
  A note on cobordisms of algebraic knots
  J. Bodnár and D. Celoria, Algebr. Geom. Topol. 17 (4), 2543 - 2564 (2017).
  • ArXiv version
  Conformal nets are factorization algebras
  A. Henriques, String-Math 2016, 229 - 239, Proc. Sympos. Pure. Math., 98, Amer. Math. Soc., Providence, RI (2018).
  • ArXiv version
  Bicommutant categories from conformal nets
  A. Henriques, preprint (2017).
  • ArXiv version
  Planar algebras in braided tensor categories
  A. Henriques, D. Penneys, and J. Tener, preprint (2016).
  • ArXiv version
  The classification of chiral WZW models by H^4_+(BG,ℤ)
  A. Henriques, Lie algebras, vertex operator algebras, and related topics, 99 - 121, Contemp. Math. 695, Amer. Math. Soc., Providence, RI (2017).
  • ArXiv version
  Defining and classifying TQFTs via surgery
  A. Juhász, Quantum Topol. 9 (2), 229 - 321 (2018).
  • ArXiv version
  Computing cobordism maps in knot Floer homology and the reduced Khovanov TQFT
  A. Juhász and M. Marengon, Selecta Math. 24 (2), 1315 - 1390 (2018).
  • ArXiv version
  Spectral order for contact manifolds with convex boundary
  A. Juhász and S. Kang, Algebr. Geom. Topol. 18 (6), 3315 - 3338 (2018).
  • ArXiv version
  Naturality and mapping class groups in Heegaard Floer homology
  A. Juhász, D. Thurston, and I. Zemke, to appear in Mem. Amer. Math. Soc. (2018).
  • ArXiv version
  Functoriality of the EH class and the LOSS invariant under Lagrangian concordances
  M. Golla and A. Juhász, preprint (2018).
  • ArXiv version
  Contact handles, duality, and sutured Floer homology
  A. Juhász and I. Zemke, preprint (2018).
  • ArXiv version
  Concordance surgery and the Ozsváth - Szabó 4-manifold invariant
  A. Juhász and I. Zemke, preprint (2018).
  • ArXiv version
  Distinguishing slice disks using knot Floer homology
  A. Juhász and I. Zemke, preprint (2018).
  • ArXiv version
  Stabilization distance bounds from link Floer homology
  A. Juhász and I. Zemke, preprint (2018).
  • ArXiv version
  A transverse link invariant from Z_2-equivariant Heegaard Floer cohomology
  S. Kang, preprint (2018).
  • ArXiv version
  Z_2-equivariant Heegaard Floer cohomology of knots in S^3 as a strong Heegaard invariant
  S. Kang, preprint (2018).
  • ArXiv version
  Heegaard Floer homology and concordance bounds on the Turston norm
  D. Celoria, M. Golla, preprint (2018).
  • ArXiv version
  Upsilon invariants from cyclic branched covers
  A. Alfieri, D. Celoria, and A. Stipsicz, preprint (2018).
  • ArXiv version
  Rational cobordisms and integral homology
  P. Aceto, D. Celoria, and J. Park, preprint (2018).
  • ArXiv version