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SUMMARY:Bob Olivier (Université Sorbonne Paris Nord)
DTSTART:20260529T150000Z
DTEND:20260529T161500Z
DTSTAMP:20260603T011819Z
UID:CIRGET/164
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CIRGET/164/"
 >The local structure of finite groups and of their classifying spaces</a>\
 nby Bob Olivier (Université Sorbonne Paris Nord) as part of CRM - Sémina
 ire du CIRGET / Géométrie et Topologie\n\nLecture held in PK-5115.\n\nAb
 stract\nFix a prime ${p}$. We say that two finite groups $G$ and\n$H$ are 
 ``${p}$-equivalent'' if there is an isomorphism between\nSylow $p$-subgrou
 ps $S \\in Syl_p(G)$ and $T\\in \nSyl_p({H})$ that preserves all $G-$ and\
 n${H}-$conjugacy relations among elements and subgroups of $S$\nand $T$. W
 e say that two topological spaces ${X}$ and ${Y}$ are ``${p}$-equivalent''
  if there is a third space ${Z}$\, and maps $X\\to Z \\leftarrow Y$ that i
 nduce isomorphisms in homology\nwith coefficients in $\\mathbb{Z}/p$. (Bot
 h of these are equivalence\nrelations.) The main theorem I want to describ
 e says that finite groups ${G}$ and ${H}$ are\n$p$-equivalent (as groups) 
 if and only if their classifying spaces\nare ${p}$-equivalent (as spaces).
 \n\n\nI will start by defining in more detail classifying spaces of discre
 te\ngroups and the two kinds of ${p}$-equivalence described above\, and\na
 lso saying a little about the background of the theorem. I then plan to\ng
 ive some examples of finite groups that are ${p}$-locally equivalent\nbut 
 not isomorphic\, and say something about ideas that went into the\nproof o
 f the theorem (carried out by several different people over a\nperiod of 1
 0--15 years).\n
LOCATION:https://researchseminars.org/talk/CIRGET/164/
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