  A fake wedge is a diagram of spaces K <- A -> C whose double mapping cylinder
is contractible. The terminology stems from the special case A = K v C with
maps given by the projections. In this paper, we study the homotopy type of the
moduli space D(K,C) of fake wedges on K and C. We formulate two conjectures
concerning this moduli space and verify that these conjectures hold after
looping once. We show how embeddings of manifolds in Euclidean space provide a
wealth of examples of non-trivial fake wedges. In an appendix, we recall
discussions that the first author had with Greg Arone and Bob Thomason in early
1995 and explain how these are related to our conjectures.
