From Heegaard splittings to trisections; porting $3$-dimensional ideas to dimension $4$

David T Gay^{1}
^{1} Euclid Lab 160 Milledge Terrace Athens, GA 30606 Department of Mathematics University of Georgia Athens, GA 30602

Winter Braids Lecture Notes, Volume 5 (2018), Talk no. 4, 19 p.

Published online:

DOI:
10.5802/wbln.24

Author's affiliations:
David T Gay ^{1}
^{1} Euclid Lab 160 Milledge Terrace Athens, GA 30606 Department of Mathematics University of Georgia Athens, GA 30602

Author's affiliations:

@article{WBLN_2018__5__A4_0, author = {David T Gay}, title = {From {Heegaard} splittings to trisections; porting $3$-dimensional ideas to dimension $4$}, journal = {Winter Braids Lecture Notes}, note = {talk:4}, publisher = {Winter Braids School}, volume = {5}, year = {2018}, doi = {10.5802/wbln.24}, language = {en}, url = {https://wbln.centre-mersenne.org/articles/10.5802/wbln.24/} }

TY - JOUR TI - From Heegaard splittings to trisections; porting $3$-dimensional ideas to dimension $4$ JO - Winter Braids Lecture Notes N1 - talk:4 PY - 2018 DA - 2018/// VL - 5 PB - Winter Braids School UR - https://wbln.centre-mersenne.org/articles/10.5802/wbln.24/ UR - https://doi.org/10.5802/wbln.24 DO - 10.5802/wbln.24 LA - en ID - WBLN_2018__5__A4_0 ER -

David T Gay. From Heegaard splittings to trisections; porting $3$-dimensional ideas to dimension $4$. Winter Braids Lecture Notes, Volume 5 (2018), Talk no. 4, 19 p. doi : 10.5802/wbln.24. https://wbln.centre-mersenne.org/articles/10.5802/wbln.24/

[1] R. İnanç Baykur; Osamu Saeki Simplified broken Lefschetz fibrations and trisections of 4-manifolds, Proceedings of the National Academy of Sciences, Volume 115 (2018) no. 43, pp. 10894-10900 http://www.pnas.org/content/115/43/10894 | http://www.pnas.org/content/115/43/10894.full.pdf | Article | MR: 3871793 | Zbl: 1421.57026

[2] Nickolas A. Castro Relative trisections of smooth 4-manifolds with boundary (2016) (Ph. D. Thesis)

[3] Nickolas A. Castro; David T. Gay; Juanita Pinzón-Caicedo Diagrams for relative trisections, Pacific J. Math., Volume 294 (2018) no. 2, pp. 275-305 | Article | MR: 3770114 | Zbl: 1394.57015

[4] David Gay; Robion Kirby Trisecting 4-manifolds, Geom. Topol., Volume 20 (2016) no. 6, pp. 3097-3132 | Article | MR: 3590351 | Zbl: 1372.57033

[5] David Gay; Jeffrey Meier Doubly pointed trisection diagrams and surgery on 2-knots, 2018 | arXiv:1806.05351

[6] András Juhász Holomorphic discs and sutured manifolds, Algebr. Geom. Topol., Volume 6 (2006), pp. 1429-1457 | Article | MR: 2253454 | Zbl: 1129.57039

[7] Robion Kirby; Abigail Thompson A new invariant of 4-manifolds, Proceedings of the National Academy of Sciences, Volume 115 (2018) no. 43, pp. 10857-10860 http://www.pnas.org/content/115/43/10857 | http://www.pnas.org/content/115/43/10857.full.pdf | Article | MR: 3871787 | Zbl: 1421.57031

[8] Peter Lambert-Cole Bridge trisections in ${\mathrm{\u2102\mathbb{P}}}^{2}$ and the Thom conjecture, 2018 | arXiv:1807.10131

[9] Peter Lambert-Cole; Jeffrey Meier Bridge trisections in rational surfaces, 2018 | arXiv:1810.10450

[10] François Laudenbach A proof of Reidemeister-Singer’s theorem by Cerf’s methods, Ann. Fac. Sci. Toulouse Math. (6), Volume 23 (2014) no. 1, pp. 197-221 | Article | Numdam | MR: 3204738 | Zbl: 1322.57020

[11] François Laudenbach; Valentin Poénaru A note on $4$-dimensional handlebodies, Bull. Soc. Math. France, Volume 100 (1972), pp. 337-344 | Article | Numdam | MR: 0317343 (47 #5890) | Zbl: 0242.57015

[12] Jeffrey Meier Trisecting surfaces filling transverse links (in preparation)

[13] Jeffrey Meier; Alexander Zupan Bridge trisections of knotted surfaces in ${S}^{4}$, Trans. Amer. Math. Soc., Volume 369 (2017) no. 10, pp. 7343-7386 | Article | MR: 3683111 | Zbl: 1376.57025

[14] Jeffrey Meier; Alexander Zupan Bridge trisections of knotted surfaces in 4-manifolds, Proceedings of the National Academy of Sciences, Volume 115 (2018) no. 43, pp. 10880-10886 http://www.pnas.org/content/115/43/10880 | http://www.pnas.org/content/115/43/10880.full.pdf | Article | MR: 3871791 | Zbl: 1418.57017

[15] Kurt Reidemeister Zur dreidimensionalen Topologie, Abh. Math. Sem. Univ. Hamburg, Volume 9 (1933) no. 1, pp. 189-194 | Article | MR: 3069596 | Zbl: 0007.08005

[16] Adam Saltz Invariants of knotted surfaces from link homology and bridge trisections, 2018 | arXiv:1809.06327

[17] James Singer Three-dimensional manifolds and their Heegaard diagrams, Trans. Amer. Math. Soc., Volume 35 (1933) no. 1, pp. 88-111 | Article | MR: 1501673 | Zbl: 0006.18501

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