There is plenty of material about winding numbers in Cauchy_Integral_Theorem. 
The theory Winding_Numbers contains more advanced and obscure results, some of 
which are direct consequences of the Jordan curve theorem, which is why they 
depend on so much other material.

Larry

> On 4 Nov 2019, at 12:48, Manuel Eberl <[email protected]> wrote:
> 
> Absolutely. The Residue theorem is the bare minimum of what I would expect to 
> be included in a development of complex analysis, and that requires winding 
> numbers.
> 
> I don't really have an idea of what material you really need for winding 
> numbers. I recall that Wenda had some problems with them (about what happens 
> when there's a pole on the path) – perhaps it would make sense to give that 
> theory an overhaul altogether? Perhaps he can chime in on this; he probably 
> knows much more about this than I do.
> 

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