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I am currently studying homology theory and am using Vicks book "Homology Theory, An introduction to algebraic topology". When I was reading I found a definition that troubles me, I simply cannot get my head around it.

Vick defines that: if PHI is a singular p-simplex we define d_{i}(PHI), a singular (p-1)-simplex in X by:

d_{i}PHI(t0, ..., t(p-1)) = PHI(t0,.., t(i-1), 0, ti,...., t(p-1))

As I see it, the PHI on the left has p arguments, and hence is a (p-1)-singular simplex while the one we end up with is a p-singular simplex since we add a zero. The "boundary operator" (i'th face operator) d_{i}is defined so we go down one dimension, but I cannot see how this works with the definition if we just fill in the rest of the arguments after we add a zero. Help please?

After some consideration I wonder if perhaps Vick should have t(i+1) on the right, but I have found other sources who uses t(i-1), 0, ti as well...

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# Definition of boundary operator

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