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.
@article{WBLN_2016__3__A4_0, author = {Takuya Sakasai}, title = {Johnson-Morita theory in mapping class groups and monoids of homology cobordisms of surfaces}, journal = {Winter Braids Lecture Notes}, note = {talk:4}, pages = {1--25}, publisher = {Winter Braids School}, volume = {3}, year = {2016}, doi = {10.5802/wbln.15}, mrnumber = {3707745}, zbl = {1422.57051}, language = {en}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/wbln.15/} }
TY - JOUR AU - Takuya Sakasai TI - Johnson-Morita theory in mapping class groups and monoids of homology cobordisms of surfaces JO - Winter Braids Lecture Notes N1 - talk:4 PY - 2016 SP - 1 EP - 25 VL - 3 PB - Winter Braids School UR - https://proceedings.centre-mersenne.org/articles/10.5802/wbln.15/ DO - 10.5802/wbln.15 LA - en ID - WBLN_2016__3__A4_0 ER -
%0 Journal Article %A Takuya Sakasai %T Johnson-Morita theory in mapping class groups and monoids of homology cobordisms of surfaces %J Winter Braids Lecture Notes %Z talk:4 %D 2016 %P 1-25 %V 3 %I Winter Braids School %U https://proceedings.centre-mersenne.org/articles/10.5802/wbln.15/ %R 10.5802/wbln.15 %G en %F WBLN_2016__3__A4_0
Takuya Sakasai. Johnson-Morita theory in mapping class groups and monoids of homology cobordisms of surfaces. Winter Braids Lecture Notes, Volume 3 (2016), Talk no. 4, 25 p. doi : 10.5802/wbln.15. https://proceedings.centre-mersenne.org/articles/10.5802/wbln.15/
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