11
$\begingroup$

I am trying to gain some intuition about retracts, deformation retracts and strong deformation retracts (see http://en.wikipedia.org/wiki/Deformation_retract for definitions). We have that any strong deformation retract is a deformation retract and any deformation retract is a retract (of course, by definition). Also, it is easy to think in a retract which is not a deformation retract.

Which are some examples of deformation retracts which are not strong deformation retracts?

  • 9
    See exercise 6 on page 18 of [Hatcher's book](http://www.math.cornell.edu/~hatcher/AT/ATpage.html). Note the difference in terminology to Wikipedia!2011-05-05
  • 0
    Similar question to this one has been asked again and an answer can be found [here](http://math.stackexchange.com/questions/281564/natural-examples-of-deformation-retracts-that-are-not-strong-deformation-retract). The same example but with more details can be found [here](http://pages.uoregon.edu/koch/math432/Solution_1.pdf).2014-04-27

1 Answers 1