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I am curious what is the common way to say (in English contexts) the name of $\partial$ (the boundary homomorphism) in homology theory. I.e. when giving a talk / speaking.

The boundary homomorphism is $\partial: C_n\to C_{n-1}$ when $(C_\bullet, \partial_\bullet)$ is a chain complex.

Some possibilities I can think of is:

  • "Boundary"?
  • "Del"?
  • "Partial"?
  • "Dee"? (it looks like a letter $d$)
  • "Delta"?

Thanks for any insights.

I haven't found any answer online despite some searching. How do you pronounce (partial) derivatives? is similar in a sense (same symbol $\partial$) but the context is entirely different.

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    The first three are all fine. The only important thing is that you're consistent and it's clear what you're referring to. – 2017-01-21
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    Basically what Mike said. I personally say 'del', and I guess the "correct" word is 'boundary'. – 2017-01-21
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    In calculus $\partial f/ \partial x$ is "die $f$ by die $x$". – 2017-01-21
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    Most of the time I say "boundary map". When I am refering to the sign $\partial$, I say "Del". – 2017-01-21
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    @user254665: (i) "die" is hopelessly ambiguous. In particular, the word "die" is not pronounced the same as "dee" in English. (ii) In any case, you have to say "_partial_ dee $f$ by dee $x$". – 2017-01-21
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    @TonyK. I have heard math profs say die f by die x. – 2017-01-22
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    @user254665: what, 'die' as in /daɪ/? I can scarcely believe that. What were their native languages? – 2017-01-22
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    die as in dead. English speakers, Americn and Canadian – 2017-01-22

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In my experience there is no single standard pronunciation, though "del" is probably the most common. I have heard all of the possibilities you suggest except "delta" used. If you want to maximize the chance that you will be understood, I would recommend just saying "(the) boundary of" rather than trying to pronounce it as a single word. In cases where you really want a shorter pronunciation, I think "del" is probably the best choice, but as Mike Miller commented the most important thing is to be consistent and unambiguous.