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J.C. Wu
J.C. Wu
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$\phi: \pi_1(S)\to \pi_1(S)$ is a homomorphism of fundamental group of closed orientable surface $S$ of genus >=2. If $\phi$ is not an epimorphism, then $\phi$ is induced bycan we find a non-surjective self map $f: S\to S$. Can induces $\phi$ such that $f(S)$ be a submanifold embedded in $S$?

$\phi: \pi_1(S)\to \pi_1(S)$ is a homomorphism of fundamental group of closed orientable surface $S$ of genus >=2. If $\phi$ is not an epimorphism, then $\phi$ is induced by a non-surjective self map $f: S\to S$. Can $f(S)$ be a submanifold embedded in $S$?

$\phi: \pi_1(S)\to \pi_1(S)$ is a homomorphism of fundamental group of closed orientable surface $S$ of genus >=2. If $\phi$ is not an epimorphism, can we find a non-surjective self map $f: S\to S$ induces $\phi$ such that $f(S)$ be a submanifold embedded in $S$?

added 24 characters in body
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J.C. Wu
J.C. Wu
  • 21
  • 2

$\phi: \pi_1(S)\to \pi_1(S)$ is a homomorphism of fundamental group of closed orientable surface $S$ of genus >=2. If $\phi$ is not an epimorphism, then $\phi$ is induced by a non-surjective self map $f: S\to S$. Can $f(S)$ be a submanifold embedded in $S$?

$\phi: \pi_1(S)\to \pi_1(S)$ is a homomorphism of fundamental group of closed surface $S$. If $\phi$ is not an epimorphism, then $\phi$ is induced by a non-surjective self map $f: S\to S$. Can $f(S)$ be a submanifold embedded in $S$?

$\phi: \pi_1(S)\to \pi_1(S)$ is a homomorphism of fundamental group of closed orientable surface $S$ of genus >=2. If $\phi$ is not an epimorphism, then $\phi$ is induced by a non-surjective self map $f: S\to S$. Can $f(S)$ be a submanifold embedded in $S$?

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J.C. Wu
J.C. Wu
  • 21
  • 2

The image of homomorphism of fundamental group of closed surface

$\phi: \pi_1(S)\to \pi_1(S)$ is a homomorphism of fundamental group of closed surface $S$. If $\phi$ is not an epimorphism, then $\phi$ is induced by a non-surjective self map $f: S\to S$. Can $f(S)$ be a submanifold embedded in $S$?