Light maps of compacta

Based on a result of H. Torunczyk, R. Pol showed that a light map f: X->Y  from a compactum X with dim X > 2 to a finite dimensional
compactum Y is injective on a non-trivial subcontinuum of X.  Pol also showed that in the above statement the restriction dim X > 2 is necessary and conjectured that some restrictions on Y are necessary as well.
All my attempts to prove/disprove Pol's conjecture failed, however some of them led to related results of independent interest having (sometimes unexpected) connections with algebraic topology that will be discussed in this talk.

This will be a joint meeting with the Algebraic Topology Seminar.