Well, to offer a somewhat garbled paraphrase T.S. "Old Possum" Elliot (see for example, http://www.americanpoems.com/poets/tseliot/5536):

You may think at first I'm as mad as a hatter

But The Naming of Things is a difficult matter,

It isn't just one of your holiday games!

Having so established my credentials in this matter, I present the following:

Think of the map $z \to z^{-1}$ as swapping charts on the Riemann sphere. (I'm OK with here, right? I mean, I haven't looked carefully at this stuff in quite awhile.) Think of the $z$-coordinate as corresponding to the North Pole. Then the $z^{-1}$- coordinate goes with the South Pole.

Now, like Ben Webster, I gots out my lil' ol' wiki hammer, yes I did, but just gave the great wiki mountain a tiny tap: what broke off was: http://en.wikipedia.org/wiki/South_Star.

The North Star is Polaris; the South Star is one Sigma Octantis.

Therefore, reminiscent, of the notion that the map $z \to z^{-1}$ is somewhat of a swap twixt north and south, how about calling your involution something based on Sigma Octantis?

List:

SigmaOctantisInvolution----way to long to type

SigOct or sigoct----shorter, not too long, you'll not likely forget it

gee, what about

$\Sigma$ or perhaps $\sigma$ ----hard to do on a keyboard; BUT there is

"sigma or perhaps just "sig"---beginning to look like "real math"!

Ah ha! Abara K'Dabara--I create as I speak! From now on, I call the involution $z \to z^{-1}$ on the algebra of Laurent polynomials $\sigma$. You could call it sig for short; if that's a reserved word in Perl use a variant like sigoct etc. Or perhaps even better, for a function in a computer language, siginv--for the sigma involution, though I'd probably just go with sig if I could.

BTW, this question inspired one of my own: http://mathoverflow.net/questions/48994/humorous-curious-unusual-names-for-mathematical-entities

HAPPY HOLIDAYS LADIES AND GENTLEMEN OF MO--HO! HO! HO!

Well, to offer a somewhat garbled paraphrase T.S. "Old Possum" Elliot (see for example, http://www.americanpoems.com/poets/tseliot/5536):

You may think at first I'm as mad as a hatter

But The Naming of Things is a difficult matter,

It isn't just one of your holiday games!

Having so established my credentials in this matter, I present the following:

Think of the map $z \to z^{-1}$ as swapping charts on the Riemann sphere. (I'm OK with here, right? I mean, I haven't looked carefully at this stuff in quite awhile.) Think of the $z$-coordinate as corresponding to the North Pole. Then the $z^{-1}$- coordinate goes with the South Pole.

Now, like Ben Webster, I gots out my lil' ol' wiki hammer, yes I did, but just gave the great wiki mountain a tiny tap: what broke off was: http://en.wikipedia.org/wiki/South_Star.

The North Star is Polaris; the South Star is one Sigma Octantis.

Therefore, reminiscent, of the notion that the map $z \to z^{-1}$ is somewhat of a swap twixt north and south, how about calling your involution something based on Sigma Octantis?

List:

SigmaOctantisInvolution----way to long to type

SigOct or sigoct----shorter, not too long, you'll not likely forget it

gee, what about

$\Sigma$ or perhaps $\sigma$ ----hard to do on a keyboard; BUT there is

"sigma or perhaps just "sig"---beginning to look like "real math"!

Ah ha! Abara K'Dabara--I create as I speak! From now on, I call the involution $z \to z^{-1}$ on the algebra of Laurent polynomials $\sigma$. You could call it sig for short; if that's a reserved word in Perl use a variant like sigoct etc. Or perhaps even better, for a function in a computer language, siginv--for the sigma involution, though I'd probably just go with sig if I could.

BTW, this question inspired one of my own: https://mathoverflow.net/questions/48994/humorous-curious-unusual-names-for-mathematical-entities

HAPPY HOLIDAYS LADIES AND GENTLEMEN OF MO--HO! HO! HO!

Well, to offer a somewhat garbled paraphrase T.S. "Old Possum" Elliot (see for example, http://www.americanpoems.com/poets/tseliot/5536):

You may think at first I'm as mad as a hatter

But The Naming of Things is a difficult matter,

It isn't just one of your holiday games!

Having so established my credentials in this matter, I present the following:

Think of the map $z \to z^{-1}$ as swapping charts on the Riemann sphere. (I'm OK with here, right? I mean, I haven't looked carefully at this stuff in quite awhile.) Think of the $z$-coordinate as corresponding to the North Pole. Then the $z^{-1}$- coordinate goes with the South Pole.

Now, like Ben Webster, I gots out my lil' ol' wiki hammer, yes I did, but just gave the great wiki mountain a tiny tap: what broke off was: http://en.wikipedia.org/wiki/South_Star.

The North Star is Polaris; the South Star is one Sigma Octantis.

Therefore, reminiscent, of the notion that the map $z \to z^{-1}$ is somewhat of a swap twixt north and south, how about calling your involution something based on Sigma Octantis?

List:

SigmaOctantisInvolution----way to long to type

SigOct or sigoct----shorter, not too long, you'll not likely forget it

gee, what about

$\Sigma$ or perhaps $\sigma$ ----hard to do on a keyboard; BUT there is

"sigma or perhaps just "sig"---beginning to look like "real math"!

Ah ha! Abara K'Dabara--I create as I speak! From now on, I call the involution $z \to z^{-1}$ on the algebra of Laurent polynomials $\sigma$. You could call it sig for short; if that's a reserved word in Perl use a variant like sigoct etc. Or perhaps even better, for a function in a computer language, siginv--for the sigma involution, though I'd probably just go with sig if I could.

HAPPY HOLIDAYS LADIES AND GENTLEMEN OF MO--HO! HO! HO!

Well, to offer a somewhat garbled paraphrase T.S. "Old Possum" Elliot (see for example, http://www.americanpoems.com/poets/tseliot/5536):

You may think at first I'm as mad as a hatter

But The Naming of Things is a difficult matter,

It isn't just one of your holiday games!

Having so established my credentials in this matter, I present the following:

Think of the map $z \to z^{-1}$ as swapping charts on the Riemann sphere. (I'm OK with here, right? I mean, I haven't looked carefully at this stuff in quite awhile.) Think of the $z$-coordinate as corresponding to the North Pole. Then the $z^{-1}$- coordinate goes with the South Pole.

Now, like Ben Webster, I gots out my lil' ol' wiki hammer, yes I did, but just gave the great wiki mountain a tiny tap: what broke off was: http://en.wikipedia.org/wiki/South_Star.

The North Star is Polaris; the South Star is one Sigma Octantis.

Therefore, reminiscent, of the notion that the map $z \to z^{-1}$ is somewhat of a swap twixt north and south, how about calling your involution something based on Sigma Octantis?

List:

SigmaOctantisInvolution----way to long to type

SigOct or sigoct----shorter, not too long, you'll not likely forget it

gee, what about

$\Sigma$ or perhaps $\sigma$ ----hard to do on a keyboard; BUT there is

"sigma or perhaps just "sig"---beginning to look like "real math"!

Ah ha! Abara K'Dabara--I create as I speak! From now on, I call the involution $z \to z^{-1}$ on the algebra of Laurent polynomials $\sigma$. You could call it sig for short; if that's a reserved word in Perl use a variant like sigoct etc. Or perhaps even better, for a function in a computer language, siginv--for the sigma involution, though I'd probably just go with sig if I could.

BTW, this question inspired one of my own: http://mathoverflow.net/questions/48994/humorous-curious-unusual-names-for-mathematical-entities

HAPPY HOLIDAYS LADIES AND GENTLEMEN OF MO--HO! HO! HO!