# Question on why a particular quasi-isomorphism between complexes doens't have an inverse

My question is on the example below, taken from page 4 of http://www.math.wisc.edu/~andreic/publications/lnPoland.pdf.

I'm not familiar enough with this stuff yet to understand why the quasi-isomorphism below does not have an inverse.

I'm also caught up on the second example since I don't understand what the map $$(x, y)$$ means. Is that projection from the first part of the direct sum onto $$\mathbb{C}[x, y]$$?

I would be appreciative if anyone here could work out the details on these examples.

• There are no nonzero maps from $Z/2$ to $Z$, for the first question. – Kevin Carlson Apr 22 at 16:55
• The obvious one is $(f,g)$ goes to $xf+yg$, but then they are quasi-isomorphic (from the second complex to the first: $f \to (yf,-xg)$, $z\to z$). – A.G Apr 22 at 20:06