From: Steve Huntsman <huntsman@cims.nyu.edu>
Subject: Re: pseudomanifolds
Date: Wed, 7 Jul 1999 02:18:56 -0400 (EDT)
Newsgroups: [missing]
To: Dave Rusin <rusin@math.niu.edu>

[deletia --djr]

Here's some info (from notes, so there may very well be errors):

X^n is called a pseudomanifold if there exists a filtration 

X^n = X_0 \contains X_2 \contains ... \contains X_n

s.t. X_k\X_(k-1) is a k-manifold for k=3...n and also s.t. X_0\X_2 = X_0.

Prototypical examples of pseudomanifolds are suspensions of manifolds,
algebraic varieties, and the following: let W be a manifold with boundary
and form W' by contracting the boundary to a point (i.e., W' = W \cup
cone(bdry W)).

From what little I can recall about this, the point of pseudomanifolds
seems to be that they're so-called stratified spaces s.t. their topology
depends in an essential way upon the stratification.

My notes center around a way to work out Poincare duality for singular
spaces, and JB probably still has most of what they say (from previous
correspondence). 

Steve Huntsman