6
$\begingroup$

I'm studying singular homology, and have come across the term acyclic. I understood that a contractible space is acyclic, but can't find a counterexample showing the inverse is false.

Could anyone suggest me (hopefully the easiest) example?

$\endgroup$
0

2 Answers 2

Reset to default
6
$\begingroup$

You can consider the exterior of the Alexander Horned Sphere. (see Hatcher-Algebraic Topology, p.169)

$\endgroup$
1
  • $\begingroup$ ah, that is a much better example :) $\endgroup$
    – Loreno Heer
    Nov 14, 2014 at 10:52
4
$\begingroup$

A counterexample is the punctured Poincare Homology Sphere.

$\endgroup$
2
  • 2
    $\begingroup$ Maybe the punctured Poincare homology sphere $\endgroup$
    – Dario
    Nov 14, 2014 at 10:46
  • $\begingroup$ @Dario fixed, thanks :) $\endgroup$
    – Loreno Heer
    Nov 14, 2014 at 10:58

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .