We give a topological proof that a free inverse monoid on one or more generators is neither of type left- nor right-. This strengthens a classical result of Schein that such monoids are not finitely presented as monoids.
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@article{CRMATH_2021__359_8_1047_0, author = {Gray, Robert D. and Steinberg, Benjamin}, title = {Free inverse monoids are not ${\protect \rm FP}_2$}, journal = {Comptes Rendus. Math\'ematique}, pages = {1047--1057}, publisher = {Acad\'emie des sciences, Paris}, volume = {359}, number = {8}, year = {2021}, doi = {10.5802/crmath.247}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/crmath.247/} }
TY - JOUR AU - Gray, Robert D. AU - Steinberg, Benjamin TI - Free inverse monoids are not ${\protect \rm FP}_2$ JO - Comptes Rendus. Mathématique PY - 2021 SP - 1047 EP - 1057 VL - 359 IS - 8 PB - Académie des sciences, Paris UR - http://archive.numdam.org/articles/10.5802/crmath.247/ DO - 10.5802/crmath.247 LA - en ID - CRMATH_2021__359_8_1047_0 ER -
%0 Journal Article %A Gray, Robert D. %A Steinberg, Benjamin %T Free inverse monoids are not ${\protect \rm FP}_2$ %J Comptes Rendus. Mathématique %D 2021 %P 1047-1057 %V 359 %N 8 %I Académie des sciences, Paris %U http://archive.numdam.org/articles/10.5802/crmath.247/ %R 10.5802/crmath.247 %G en %F CRMATH_2021__359_8_1047_0
Gray, Robert D.; Steinberg, Benjamin. Free inverse monoids are not ${\protect \rm FP}_2$. Comptes Rendus. Mathématique, Volume 359 (2021) no. 8, pp. 1047-1057. doi : 10.5802/crmath.247. http://archive.numdam.org/articles/10.5802/crmath.247/
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