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SUMMARY:Andrei Jaikin-Zapirain (Autonomous University of Madrid)
DTSTART:20201015T150000Z
DTEND:20201015T160000Z
DTSTAMP:20260423T021442Z
UID:GOThIC/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GOThIC/2/">I
 ntersection of subgroups in a surface group</a>\nby Andrei Jaikin-Zapirain
  (Autonomous University of Madrid) as part of GOThIC - Ischia Online Group
  Theory Conference\n\n\nAbstract\nLet $G$ be a surface group\, i.e the fun
 damental group of a compact surface. Denote by $d(G)$ the number of genera
 tors of $G$ and by $\\chi(G)$ the Euler characteristic of $G$. We put $\\b
 ar \\chi(G) = \\max\\{0\, −\\chi(G)\\}$.\n\nIn this talk I will explain 
 the following two results. In the first result we prove that for any two f
 initely generated subgroups $U$ and $W$ of $G$\,\n\n$$\n\\sum_{x \\in U\\b
 ackslash G / W} \\bar \\chi (U \\cap x W x^{-1}) \\le \\bar \\chi(U) \\cdo
 t \\bar\\chi(W).\n$$\nFrom this we obtain the Strengthened Hanna Neumann c
 onjecture for non-solvable surface groups. In the second result we show th
 at if $R$ is a retract of $G$\, then for any finitely generated subgroup $
 H$ of $G$\,\n$$\nd(R \\cap H) \\le d(H).\n$$\nThis implies the Dicks-Ventu
 ra inertia conjecture for free groups. The talk is based on a joint work w
 ith Yago Antolín.\n
LOCATION:https://researchseminars.org/talk/GOThIC/2/
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