Consider $D^2$, remove two open balls from the interior, and glue two copies of $S^1$'s along the boundaries of these two holes, according to the maps $z \mapsto z^p$, and $z \mapsto z^q$ for distinct primes $p,q$. For example, I'm attaching a picture of how it might look for the case $p=2$, $q=3$:
Can this space be retracted to it's boundary? I have heard this mentioned in passing by someone, but never understood why. Is this even true?