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Trisection diagrams and twists of 4-manifolds
Patrick Naylor1
1 Department of Mathematics, Princeton University, Princeton NJ 08544, USA
Comptes Rendus. Mathématique, Volume 360 (2022), 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

Patrick Naylor 1

1 Department of Mathematics, Princeton University, Princeton NJ 08544, USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Patrick Naylor. Trisection diagrams and twists of 4-manifolds. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 845-866. doi : 10.5802/crmath.350. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.350/

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

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

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

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

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

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

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

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

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

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

[11] Atsuko Katanaga; Osamu Saeki; Masakazu Teragaito; Yuichi Yamada 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] Seungwon Kim; Maggie Miller Trisections of surface complements and the Price twist, Algebr. Geom. Topol., Volume 20 (2020) no. 1, pp. 343-373

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

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

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

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

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

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

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

[20] Thomas M. Price 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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