  The absolute order is a natural partial order on a Coxeter group W. It can be
viewed as an analogue of the weak order on W in which the role of the
generating set of simple reflections in W is played by the set of all
reflections in W. By use of a notion of constructibility for partially ordered
sets, it is proved that the absolute order on the symmetric group is homotopy
Cohen-Macaulay. This answers in part a question raised by V. Reiner and the
first author. The Euler characteristic of the order complex of the proper part
of the absolute order on the symmetric group is also computed.
