@article{PRT2025,
  author        = {Powell, Mark and Ray, Arunima and Teichner, Peter},
  title         = {The {4}-dimensional disc embedding theorem and dual spheres},
  journal       = {Selecta Mathematica. New Series},
  volume        = {31},
  number        = {4},
  year          = {2025},
  eid           = {80},
  pages         = {Paper No. 80},
  note          = {25 pp.},
  doi           = {10.1007/s00029-025-01069-y},
  eprint        = {2006.05209},
  archivePrefix = {arXiv},
  primaryClass  = {math.GT},
  url           = {https://doi.org/10.1007/s00029-025-01069-y}
}

@article{Freedman1982,
  author  = {Freedman, Michael H.},
  title   = {The topology of four-dimensional manifolds},
  journal = {Journal of Differential Geometry},
  volume  = {17},
  number  = {3},
  year    = {1982},
  pages   = {357--453},
  doi     = {10.4310/jdg/1214437136},
  url     = {https://doi.org/10.4310/jdg/1214437136}
}

@book{FQ1990,
  author    = {Freedman, Michael H. and Quinn, Frank},
  title     = {Topology of {4}-manifolds},
  series    = {Princeton Mathematical Series},
  volume    = {39},
  publisher = {Princeton University Press},
  address   = {Princeton, NJ},
  year      = {1990},
  isbn      = {0-691-08577-3},
  doi       = {10.1515/9781400861064},
  url       = {https://doi.org/10.1515/9781400861064}
}

@article{FT1995,
  author  = {Freedman, Michael H. and Teichner, Peter},
  title   = {{4}-manifold topology. {I}. {Subexponential} groups},
  journal = {Inventiones Mathematicae},
  volume  = {122},
  year    = {1995},
  pages   = {509--529},
  doi     = {10.1007/BF01231454},
  url     = {https://doi.org/10.1007/BF01231454}
}

@article{KQ2000,
  author        = {Krushkal, Vyacheslav S. and Quinn, Frank},
  title         = {Subexponential groups in {4}-manifold topology},
  journal       = {Geometry \& Topology},
  volume        = {4},
  year          = {2000},
  pages         = {407--430},
  note          = {With an appendix by Michael H. Freedman and Peter Teichner},
  doi           = {10.2140/gt.2000.4.407},
  eprint        = {math/0001063},
  archivePrefix = {arXiv},
  primaryClass  = {math.GT},
  url           = {https://doi.org/10.2140/gt.2000.4.407}
}

@incollection{KOPR2021,
  author    = {Kim, Min Hoon and Orson, Patrick and Park, JungHwan and Ray, Arunima},
  title     = {Open problems},
  booktitle = {The Disc Embedding Theorem},
  editor    = {Behrens, Stefan and Kalm\'{a}r, Boldizs\'{a}r and Kim, Min Hoon
               and Powell, Mark and Ray, Arunima},
  publisher = {Oxford University Press},
  address   = {Oxford},
  year      = {2021},
  chapter   = {23},
  pages     = {353--382},
  doi       = {10.1093/oso/9780198841319.003.0023},
  url       = {https://doi.org/10.1093/oso/9780198841319.003.0023}
}

@article{DSGJ2020,
  author        = {De Stefani, Alessandro and Grifo, Elo\'{i}sa and Jeffries, Jack},
  title         = {A {Zariski--Nagata} theorem for smooth {$\mathbb{Z}$}-algebras},
  journal       = {Journal f\"ur die reine und angewandte Mathematik},
  volume        = {761},
  year          = {2020},
  pages         = {123--140},
  doi           = {10.1515/crelle-2018-0012},
  eprint        = {1709.01049v3},
  note          = {Theorem and Lemma numbering refers to arXiv:1709.01049v3},
  archivePrefix = {arXiv},
  primaryClass  = {math.AC},
  url           = {https://doi.org/10.1515/crelle-2018-0012}
}

@misc{Stacks,
  author       = {{The Stacks Project Authors}},
  title        = {The Stacks Project},
  year         = {2026},
  howpublished = {\url{https://stacks.math.columbia.edu}},
  note         = {Permanent tags cited in the text; accessed 18 September 2026},
  url          = {https://stacks.math.columbia.edu}
}

@book{Hatcher2002,
  author    = {Hatcher, Allen},
  title     = {Algebraic Topology},
  publisher = {Cambridge University Press},
  address   = {Cambridge},
  year      = {2002},
  isbn      = {0-521-79540-0},
  url       = {https://pi.math.cornell.edu/~hatcher/AT/ATpage.html}
}

@article{ChernSimons1974,
  author  = {Chern, Shiing-Shen and Simons, James},
  title   = {Characteristic forms and geometric invariants},
  journal = {Annals of Mathematics. Second Series},
  volume  = {99},
  number  = {1},
  year    = {1974},
  pages   = {48--69},
  doi     = {10.2307/1971013},
  url     = {https://annals.math.princeton.edu/1974/99-1/p03}
}

@book{Milnor1965,
  author    = {Milnor, John W.},
  title     = {Topology from the Differentiable Viewpoint},
  publisher = {University Press of Virginia},
  address   = {Charlottesville},
  year      = {1965}
}

@article{GM1988,
  author  = {Goldman, William M. and Millson, John J.},
  title   = {The deformation theory of representations of fundamental groups of compact {K\"ahler} manifolds},
  journal = {Publications Math\'ematiques de l'IH\'ES},
  volume  = {67},
  year    = {1988},
  pages   = {43--96},
  doi     = {10.1007/BF02699127},
  url     = {https://doi.org/10.1007/BF02699127}
}

@article{Koszul1950,
  author  = {Koszul, Jean-Louis},
  title   = {Homologie et cohomologie des alg\`ebres de {Lie}},
  journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
  volume  = {78},
  year    = {1950},
  pages   = {65--127},
  doi     = {10.24033/bsmf.1410},
  url     = {https://numdam.org/articles/10.24033/bsmf.1410/}
}

@article{Katz1970,
  author  = {Katz, Nicholas M.},
  title   = {Nilpotent connections and the monodromy theorem: applications of a result of {Turrittin}},
  journal = {Publications Math\'ematiques de l'IH\'ES},
  volume  = {39},
  year    = {1970},
  pages   = {175--232},
  doi     = {10.1007/BF02684688},
  url     = {https://numdam.org/articles/10.1007/BF02684688/}
}

@article{Freedman1986AB,
  author  = {Freedman, Michael H.},
  title   = {Are the {Borromean} rings {$A$--$B$}-slice?},
  journal = {Topology and its Applications},
  volume  = {24},
  number  = {1--3},
  year    = {1986},
  pages   = {143--145},
  doi     = {10.1016/0166-8641(86)90055-6},
  url     = {https://doi.org/10.1016/0166-8641(86)90055-6}
}

@article{FL1989,
  author  = {Freedman, Michael H. and Lin, Xiao-Song},
  title   = {On the {$(A,B)$}-slice problem},
  journal = {Topology},
  volume  = {28},
  number  = {1},
  year    = {1989},
  pages   = {91--110},
  doi     = {10.1016/0040-9383(89)90034-7},
  url     = {https://doi.org/10.1016/0040-9383(89)90034-7}
}

@article{Krushkal2008,
  author  = {Krushkal, Vyacheslav S.},
  title   = {A counterexample to the strong version of {Freedman's} conjecture},
  journal = {Annals of Mathematics. Second Series},
  volume  = {168},
  number  = {2},
  year    = {2008},
  pages   = {675--693},
  doi     = {10.4007/annals.2008.168.675},
  url     = {https://annals.math.princeton.edu/2008/168-2/p07}
}

@article{FK2016,
  author  = {Freedman, Michael H. and Krushkal, Vyacheslav S.},
  title   = {Engel relations in {$4$}-manifold topology},
  journal = {Forum of Mathematics, Sigma},
  volume  = {4},
  year    = {2016},
  pages   = {e22},
  note    = {57 pp.},
  doi     = {10.1017/fms.2016.20},
  url     = {https://doi.org/10.1017/fms.2016.20}
}

@article{KL2002,
  author  = {Krushkal, Vyacheslav S. and Lee, Ronnie},
  title   = {Surgery on closed {$4$}-manifolds with free fundamental group},
  journal = {Mathematical Proceedings of the Cambridge Philosophical Society},
  volume  = {133},
  number  = {2},
  year    = {2002},
  pages   = {305--310},
  doi     = {10.1017/S0305004102006084},
  url     = {https://doi.org/10.1017/S0305004102006084}
}

@article{KPT2021,
  author        = {Kim, Min Hoon and Powell, Mark and Teichner, Peter},
  title         = {Round handle problem},
  journal       = {Pure and Applied Mathematics Quarterly},
  volume        = {17},
  number        = {1},
  year          = {2021},
  pages         = {237--247},
  doi           = {10.4310/PAMQ.2021.v17.n1.a6},
  eprint        = {1706.09571},
  archivePrefix = {arXiv},
  primaryClass  = {math.GT},
  url           = {https://doi.org/10.4310/PAMQ.2021.v17.n1.a6}
}