This article is the notes of a series of lectures in the workshop “Winter Braids VI”, Lille, in February 2016. We begin by recalling fundamental facts on mapping class groups of surfaces and overview the theory of Johnson homomorphisms developed by Johnson himself and Morita. Then we see how this theory is extended as invariants of homology cobordisms of surfaces and discuss an application to knot theory.
Mots-clés : Mapping class group; Torelli group; Johnson homomorphism; homology cobordism.
@article{WBLN_2016__3__A4_0, author = {Sakasai, Takuya}, title = {Johnson-Morita theory in mapping class groups and monoids of homology cobordisms of surfaces}, booktitle = {Winter Braids VI (Lille, 2016)}, series = {Winter Braids Lecture Notes}, note = {talk:4}, pages = {1--25}, publisher = {Winter Braids School}, year = {2016}, doi = {10.5802/wbln.15}, mrnumber = {3707745}, zbl = {1422.57051}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/wbln.15/} }
TY - JOUR AU - Sakasai, Takuya TI - Johnson-Morita theory in mapping class groups and monoids of homology cobordisms of surfaces BT - Winter Braids VI (Lille, 2016) AU - Collectif T3 - Winter Braids Lecture Notes N1 - talk:4 PY - 2016 SP - 1 EP - 25 PB - Winter Braids School UR - http://archive.numdam.org/articles/10.5802/wbln.15/ DO - 10.5802/wbln.15 LA - en ID - WBLN_2016__3__A4_0 ER -
%0 Journal Article %A Sakasai, Takuya %T Johnson-Morita theory in mapping class groups and monoids of homology cobordisms of surfaces %B Winter Braids VI (Lille, 2016) %A Collectif %S Winter Braids Lecture Notes %Z talk:4 %D 2016 %P 1-25 %I Winter Braids School %U http://archive.numdam.org/articles/10.5802/wbln.15/ %R 10.5802/wbln.15 %G en %F WBLN_2016__3__A4_0
Sakasai, Takuya. Johnson-Morita theory in mapping class groups and monoids of homology cobordisms of surfaces, in Winter Braids VI (Lille, 2016), Winter Braids Lecture Notes (2016), Talk no. 4, 25 p. doi : 10.5802/wbln.15. http://archive.numdam.org/articles/10.5802/wbln.15/
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