Timeline for embeddings of graphs into surfaces

10 events

when toggle format	what		by	license	comment
Jun 18, 2013 at 18:45	vote	accept	Misha
Jun 18, 2013 at 18:45	vote	accept	Misha
Jun 18, 2013 at 18:45
Jun 18, 2013 at 16:46	comment	added	Misha		Lee: Yes, this was the motivation.
Jun 18, 2013 at 16:15	comment	added	Lee Mosher		Regarding question 1, your two assumptions together imply that $rank(\Gamma)=2genus(S)$, because the first says $1−r \ge 1−2g$ and surjectivity of $i_∗$ implies $r \ge 2g$. Is that the intent?
Jun 18, 2013 at 16:07	answer	added	Bruno Martelli		timeline score: 9
Jun 18, 2013 at 12:11	history	edited	Misha	CC BY-SA 3.0	added surjectivity assumption
Jun 18, 2013 at 12:06	comment	added	Misha		@Bruno: You are absolutely right, this is impossible (one sees this by lifting maps to the universal cover). I am interested in maps which induce epimorphisms of fundamental groups, so I will add this to the question.
Jun 18, 2013 at 10:51	comment	added	Bruno Martelli		I make a simple modification of your example, just to understand the problem. Take $\Gamma = K_5$ and $\Gamma'$ the rose with 6 petals. Embed $\Gamma'$ in a disc contained in a surface $S$ with large genus. To answer your question positively you need to embed $K_5$ in $S$ with a map which is homotopic to a costant map. But that sounds impossible to me.
Jun 18, 2013 at 3:32	history	edited	Misha	CC BY-SA 3.0	edited body
Jun 18, 2013 at 3:10	history	asked	Misha	CC BY-SA 3.0