mike wrote :
I asked my neighbor to prune the trees that overhang my house.
Was told to go pound sand.
So, the offending branch is about 20 feet up.
I don't have a ladder tall enough to get at it
safely with a chain saw.
I'd rather not try to chop it off at the trunk for fear it
will land on my TV antenna and bust it.

I tried throwing a rope over it last summer to see if I could break it.
I think I can pull at an angle so it falls between the houses.
Didn't break.

It's gonna be 18F here tomorrow. That's about as cold as it ever gets.

What's the dynamic if I pull down on it when it's cold outside?
Likely to break easier? It's about 2" diameter where I'd like it
to break.

No, I don't know what kind of tree it is. Some version of
maple, maybe...no leaves on it now. It's not in particularly
good health. Lots of decay.

Is there anything interesting I can do without hurting myself?

This is not an answer to your question, but it might be a good idea to
contact a lawyer and have them send a formal request to your neighbor.
Not to threaten them, but to document that you had requested the
trimming. That way when it falls and causes damage, your neighbor will
be liable for damages rather than being SOL for an Act Of God.