* Answers
@ 1998-07-20 17:20 Michael Barr
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From: Michael Barr @ 1998-07-20 17:20 UTC (permalink / raw)
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I got the same counter-example from Peter Johnstone and Peter Freyd. PJ
called it the dunce cap and described it as a triangle with the three
edges identified, one in the reverse direction. PF described it in a more
complicated way that made it easier to see it actually contractible. And
the latter was really what I wanted to refute. When I saw PJ's example, I
mistakenly thought it still had a 1-cycle.
The smallest triangulation I found had 8 vertices, which is still too
large to compute by hand with. The dual complex still has over 200
simplexes and that is just too many. If anyone knows a smaller
triangulation, I would like to know it.
Thanks to all who responded.
Michael
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1998-07-20 17:20 Answers Michael Barr
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