Géométrie et Topologie
Trisection diagrams and twists of 4-manifolds
Comptes Rendus. Mathématique, Tome 360 (2022) no. G8, pp. 845-866.

Un théorème de Katanaga, Saeki, Teragaito, et Yamada établit une connexion entre des torsions de Gluck et Price. On donne une nouvelle démonstration de ce théorème en utilisant des diagrammes de trisection, et on répond à une question de Kim et Miller.

A theorem of Katanaga, Saeki, Teragaito, and Yamada relates Gluck and Price twists of 4-manifolds. Using trisection diagrams, we give a purely diagrammatic proof of this theorem, and answer a question of Kim and Miller.

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DOI : 10.5802/crmath.350
Naylor, Patrick 1

1 Department of Mathematics, Princeton University, Princeton NJ 08544, USA
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Naylor, Patrick. Trisection diagrams and twists of 4-manifolds. Comptes Rendus. Mathématique, Tome 360 (2022) no. G8, pp. 845-866. doi : 10.5802/crmath.350. http://www.numdam.org/articles/10.5802/crmath.350/

[1] Akbulut, Selman Twisting 4-manifolds along 2 , Proceedings of the 16th Gökova geometry-topology conference, International Press, 2010, pp. 137-141 | Zbl

[2] Castro, Nickolas A. Relative trisections of smooth 4-manifolds with boundary, Ph. D. Thesis, University of Georgia (2015)

[3] Castro, Nickolas A.; Gay, David; Pinzón-Caicedo, Juanita Diagrams for relative trisections, Pac. J. Math., Volume 294 (2018) no. 2, pp. 275-305 | MR | Zbl

[4] Castro, Nickolas A.; Gay, David; Pinzón-Caicedo, Juanita Trisections of 4-manifolds with boundary, Proc. Natl. Acad. Sci. USA, Volume 115 (2018) no. 43, pp. 10861-10868 | DOI | MR

[5] Castro, Nickolas A.; Islambouli, Gabriel; Miller, Maggie; Tomova, Maggy The relative -invariant of a compact 4-manifold (2019) | arXiv

[6] Freedman, Michael Hartley The topology of four-dimensional manifolds, J. Differ. Geom., Volume 17 (1982) no. 3, pp. 357-453 | DOI | MR | Zbl

[7] Gay, David; Kirby, Robion Trisecting 4-manifolds, Geom. Topol., Volume 20 (2016) no. 6, pp. 3097-3132 | MR | Zbl

[8] Gay, David; Meier, Jeffrey Doubly pointed trisection diagrams and surgery on 2-knots (2018) | arXiv

[9] Gluck, Herman The embedding of two-spheres in the four-sphere, Bull. Am. Math. Soc., Volume 67 (1961) no. 6, pp. 586-589 | MR | Zbl

[10] Hughes, Mark; Kim, Seungwon; Miller, Maggie Isotopies of surfaces in 4–manifolds via banded unlink diagrams, Geom. Topol., Volume 24 (2020) no. 3, pp. 1519-1569

[11] Katanaga, Atsuko; Saeki, Osamu; Teragaito, Masakazu; Yamada, Yuichi et al. Gluck surgery along a 2-sphere in a 4-manifold is realized by surgery along a projective plane., Mich. Math. J., Volume 46 (1999) no. 3, pp. 555-571

[12] Kim, Seungwon; Miller, Maggie Trisections of surface complements and the Price twist, Algebr. Geom. Topol., Volume 20 (2020) no. 1, pp. 343-373

[13] Lambert-Cole, Peter Bridge trisections in ℂℙ 2 and the Thom conjecture, Geom. Topol., Volume 24 (2020) no. 3, pp. 1571-1614

[14] Lambert-Cole, Peter Trisections, intersection forms and the Torelli group, Algebr. Geom. Topol., Volume 20 (2020) no. 2, pp. 1015-1040

[15] Laudenbach, François; Poénaru, Valentin A note on 4-dimensional handlebodies, Bull. Soc. Math. Fr., Volume 100 (1972), pp. 337-344

[16] Massey, William Proof of a conjecture of Whitney, Pac. J. Math., Volume 31 (1969) no. 1, pp. 143-156

[17] Meier, Jeffrey; Schirmer, Trent; Zupan, Alexander Classification of trisections and the generalized property R conjecture, Proc. Am. Math. Soc., Volume 144 (2016) no. 11, pp. 4983-4997

[18] Meier, Jeffrey; Zupan, Alexander Bridge trisections of knotted surfaces in S 4 , Trans. Am. Math. Soc., Volume 369 (2017) no. 10, pp. 7343-7386

[19] Meier, Jeffrey; Zupan, Alexander Bridge trisections of knotted surfaces in 4-manifolds, Proc. Natl. Acad. Sci. USA, Volume 115 (2018) no. 43, pp. 10880-10886

[20] Price, Thomas M. Homeomorphisms of quaternion space and projective planes in four space, J. Aust. Math. Soc., Volume 23 (1977) no. 1, pp. 112-128

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