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Homotopic symbol

Moderators: helmut, Shadow, outermeasure, Ilaggoodly

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Shadow

Post subject: Homotopic symbol

Posted: Fri, 7 May 2010 18:42:24 UTC

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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12097
Location: Austin, TX

So I know $\cong$ and $\equiv$ are

Code:

\cong

and

Code:

\equiv

, but what is the syntax for the $\cong$ with only one bar underneath it?

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outermeasure

Post subject: Re: Homotopic symbol

Posted: Fri, 7 May 2010 18:50:46 UTC

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Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6005
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Shadow wrote:

So I know $\cong$ and $\equiv$ are

Code:

\cong

and

Code:

\equiv

, but what is the syntax for the $\cong$ with only one bar underneath it?

$\simeq$ is

Code:

\simeq

, no need for any additional packages.

A good(?) rule of thumb: (...)eq is one line underneath, e.g. $\subseteq$ and $\preceq$ )

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$\begin{aligned} Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\ Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\ Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\ Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\ Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\ Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4 \end{aligned}$

Last edited by outermeasure on Fri, 7 May 2010 18:53:36 UTC, edited 1 time in total.

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Shadow

Post subject:

Posted: Fri, 7 May 2010 18:50:59 UTC

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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12097
Location: Austin, TX

Many thanks!

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Matt

Post subject:

Posted: Fri, 7 May 2010 18:59:00 UTC

Member of the 'S.O.S. Math' Hall of Fame

Joined: Wed, 1 Oct 2003 04:45:43 UTC
Posts: 9632

For your future math needs, you might like to check out:

http://detexify.kirelabs.org/classify.html

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Shadow

Post subject:

Posted: Fri, 7 May 2010 19:44:31 UTC

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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12097
Location: Austin, TX

Matt wrote:

For your future math needs, you might like to check out:

http://detexify.kirelabs.org/classify.html

Matt, you are now my all time favorite person!

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