# morse reduction

I was reading the paper by Mischaikow and was confused by how the MorseReduce function would run, particularly what the output would be.

Say I had a triangle with a simplex-wise filtration as given

  1
4/ \5
2 - 3
6


How would the algorithm execute?

I did some calculations and I get that the "aces"/critical cells are 1 and 6 and we get the queen/king pairs: (2,4), (3,5).

but how do we then represent the new boundary matrix on this complex?

Is 6 somehow connected to 1 at both its ends? That doesn't make any sense to me.