L’objectif de ce texte est de présenter la notion de systole d’une variété riemannienne et de faire un survol de la géométrie systolique. On illustrera aussi une technique fondamentale, appelée technique de régularisation, qui est à la base de plusieurs résultats essentiels de géométrie systolique. Je détaillerai comment cette technique permet d’estimer les nombres de Betti d’une variété asphérique (d’après Gromov), et comment elle permet de relier l’entropie volumique à la systole et au volume systolique d’une variété riemannienne (d’après Sabourau).
@article{TSG_2012-2014__31__1_0, author = {Bulteau, Guillaume}, title = {G\'eom\'etrie systolique et technique de r\'egularisation}, journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie}, pages = {1--41}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {31}, year = {2012-2014}, doi = {10.5802/tsg.292}, language = {fr}, url = {http://archive.numdam.org/articles/10.5802/tsg.292/} }
TY - JOUR AU - Bulteau, Guillaume TI - Géométrie systolique et technique de régularisation JO - Séminaire de théorie spectrale et géométrie PY - 2012-2014 SP - 1 EP - 41 VL - 31 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/tsg.292/ DO - 10.5802/tsg.292 LA - fr ID - TSG_2012-2014__31__1_0 ER -
%0 Journal Article %A Bulteau, Guillaume %T Géométrie systolique et technique de régularisation %J Séminaire de théorie spectrale et géométrie %D 2012-2014 %P 1-41 %V 31 %I Institut Fourier %C Grenoble %U http://archive.numdam.org/articles/10.5802/tsg.292/ %R 10.5802/tsg.292 %G fr %F TSG_2012-2014__31__1_0
Bulteau, Guillaume. Géométrie systolique et technique de régularisation. Séminaire de théorie spectrale et géométrie, Tome 31 (2012-2014), pp. 1-41. doi : 10.5802/tsg.292. http://archive.numdam.org/articles/10.5802/tsg.292/
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