Nous prouvons que la variété de dimension 3 obtenue en recollant les complémentaires de deux nœuds non triviaux dans des -espaces instantoniques qui sont des sphères d’homologie, par une application qui identifie les méridiens avec les longitudes de Seifert, ne peut pas être un -espace instantonique. Cela redémontre le théorème récent de Lidman–Pinzón-Caicedo–Zentner selon lequel le groupe fondamental de toute variété fermée orientée toroïdale de dimension 3 admet une -représentation non triviale, et par conséquent le résultat précédent de Zentner que le groupe fondamental de toute variété de dimension 3 fermée orientée différente de la sphère admet une représentation non triviale dans .
We prove that the 3-manifold obtained by gluing the complements of two nontrivial knots in homology 3-sphere instanton -spaces, by a map which identifies meridians with Seifert longitudes, cannot be an instanton -space. This recovers the recent theorem of Lidman–Pinzón-Caicedo–Zentner that the fundamental group of every closed, oriented, toroidal 3-manifold admits a nontrivial -representation, and consequently Zentner’s earlier result that the fundamental group of every closed, oriented -manifold besides the 3-sphere admits a nontrivial -representation.
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Mots clés : Instanton Floer homology, L-spaces, incompressible tori
@article{AHL_2022__5__1213_0, author = {Baldwin, John A. and Sivek, Steven}, title = {Instanton $L$-spaces and splicing}, journal = {Annales Henri Lebesgue}, pages = {1213--1233}, publisher = {\'ENS Rennes}, volume = {5}, year = {2022}, doi = {10.5802/ahl.148}, language = {en}, url = {http://www.numdam.org/articles/10.5802/ahl.148/} }
Baldwin, John A.; Sivek, Steven. Instanton $L$-spaces and splicing. Annales Henri Lebesgue, Tome 5 (2022), pp. 1213-1233. doi : 10.5802/ahl.148. http://www.numdam.org/articles/10.5802/ahl.148/
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