These notes summarize and expand on a mini-course given at CIRM in February 2018 as part of Winter Braids VIII. We somewhat obsessively develop the slogan “Trisections are to –manifolds as Heegaard splittings are to –manifolds”, focusing on and clarifying the distinction between three ways of thinking of things: the basic definitions as decompositions of manifolds, the Morse theoretic perspective and descriptions in terms of diagrams. We also lay out these themes in two important relative settings: –manifolds with boundary and –manifolds with embedded –dimensional submanifolds.
@article{WBLN_2018__5__A4_0, author = {Gay, David T}, title = {From {Heegaard} splittings to trisections; porting $3$-dimensional ideas to dimension $4$}, booktitle = {Winter Braids VIII (Marseille, 2018)}, series = {Winter Braids Lecture Notes}, note = {talk:4}, pages = {1--19}, publisher = {Winter Braids School}, year = {2018}, doi = {10.5802/wbln.24}, language = {en}, url = {http://www.numdam.org/articles/10.5802/wbln.24/} }
TY - JOUR AU - Gay, David T TI - From Heegaard splittings to trisections; porting $3$-dimensional ideas to dimension $4$ BT - Winter Braids VIII (Marseille, 2018) AU - Collectif T3 - Winter Braids Lecture Notes N1 - talk:4 PY - 2018 SP - 1 EP - 19 PB - Winter Braids School UR - http://www.numdam.org/articles/10.5802/wbln.24/ DO - 10.5802/wbln.24 LA - en ID - WBLN_2018__5__A4_0 ER -
%0 Journal Article %A Gay, David T %T From Heegaard splittings to trisections; porting $3$-dimensional ideas to dimension $4$ %B Winter Braids VIII (Marseille, 2018) %A Collectif %S Winter Braids Lecture Notes %Z talk:4 %D 2018 %P 1-19 %I Winter Braids School %U http://www.numdam.org/articles/10.5802/wbln.24/ %R 10.5802/wbln.24 %G en %F WBLN_2018__5__A4_0
Gay, David T. From Heegaard splittings to trisections; porting $3$-dimensional ideas to dimension $4$, in Winter Braids VIII (Marseille, 2018), Winter Braids Lecture Notes (2018), Talk no. 4, 19 p. doi : 10.5802/wbln.24. http://www.numdam.org/articles/10.5802/wbln.24/
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