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.
Révisé le :
Accepté le :
Publié le :
@article{CRMATH_2022__360_G8_845_0, author = {Naylor, Patrick}, title = {Trisection diagrams and twists of 4-manifolds}, journal = {Comptes Rendus. Math\'ematique}, pages = {845--866}, publisher = {Acad\'emie des sciences, Paris}, volume = {360}, number = {G8}, year = {2022}, doi = {10.5802/crmath.350}, language = {en}, url = {http://www.numdam.org/articles/10.5802/crmath.350/} }
TY - JOUR AU - Naylor, Patrick TI - Trisection diagrams and twists of 4-manifolds JO - Comptes Rendus. Mathématique PY - 2022 SP - 845 EP - 866 VL - 360 IS - G8 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.350/ DO - 10.5802/crmath.350 LA - en ID - CRMATH_2022__360_G8_845_0 ER -
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] Twisting 4-manifolds along , Proceedings of the 16th Gökova geometry-topology conference, International Press, 2010, pp. 137-141 | Zbl
[2] Relative trisections of smooth 4-manifolds with boundary, Ph. D. Thesis, University of Georgia (2015)
[3] Diagrams for relative trisections, Pac. J. Math., Volume 294 (2018) no. 2, pp. 275-305 | MR | Zbl
[4] Trisections of 4-manifolds with boundary, Proc. Natl. Acad. Sci. USA, Volume 115 (2018) no. 43, pp. 10861-10868 | DOI | MR
[5] The relative -invariant of a compact -manifold (2019) | arXiv
[6] The topology of four-dimensional manifolds, J. Differ. Geom., Volume 17 (1982) no. 3, pp. 357-453 | DOI | MR | Zbl
[7] Trisecting 4-manifolds, Geom. Topol., Volume 20 (2016) no. 6, pp. 3097-3132 | MR | Zbl
[8] Doubly pointed trisection diagrams and surgery on 2-knots (2018) | arXiv
[9] The embedding of two-spheres in the four-sphere, Bull. Am. Math. Soc., Volume 67 (1961) no. 6, pp. 586-589 | MR | Zbl
[10] Isotopies of surfaces in 4–manifolds via banded unlink diagrams, Geom. Topol., Volume 24 (2020) no. 3, pp. 1519-1569
[11] 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] Trisections of surface complements and the Price twist, Algebr. Geom. Topol., Volume 20 (2020) no. 1, pp. 343-373
[13] Bridge trisections in and the Thom conjecture, Geom. Topol., Volume 24 (2020) no. 3, pp. 1571-1614
[14] Trisections, intersection forms and the Torelli group, Algebr. Geom. Topol., Volume 20 (2020) no. 2, pp. 1015-1040
[15] A note on 4-dimensional handlebodies, Bull. Soc. Math. Fr., Volume 100 (1972), pp. 337-344
[16] Proof of a conjecture of Whitney, Pac. J. Math., Volume 31 (1969) no. 1, pp. 143-156
[17] Classification of trisections and the generalized property R conjecture, Proc. Am. Math. Soc., Volume 144 (2016) no. 11, pp. 4983-4997
[18] Bridge trisections of knotted surfaces in , Trans. Am. Math. Soc., Volume 369 (2017) no. 10, pp. 7343-7386
[19] Bridge trisections of knotted surfaces in 4-manifolds, Proc. Natl. Acad. Sci. USA, Volume 115 (2018) no. 43, pp. 10880-10886
[20] Homeomorphisms of quaternion space and projective planes in four space, J. Aust. Math. Soc., Volume 23 (1977) no. 1, pp. 112-128
Cité par Sources :