codimension k stratum

[seydunas]

Hi

What do you understand from this sentence: manifold with corners whose codimension k stratum? i am reading the lecture notes by Hutchings, Morse Homology. When i see the compactification theorem of modili spaces, i read a this sentence but i understood nothing.

[quasar987]

I've been wondering about that also. Post the answer here if you find out please.

[seydunas]

Hi,

i found a definition of codimension k-stratum. We define the codimension k-stratum of X to be the set X_k of points x in X with a chart f : U---> R^n-k x [0, infinity)^k such that at least one of the last k-coordinates of f(x) is zero.
Note that X_0 is just the interior of X.

I wonder that if you prove the "Compactification of moduli space" in Hutchings Lecture note, can you give me some hints, or direct detail.