Goal: I am trying to find a way to write an equation for:

However, I fail, or at least so far could not find a way, to add the last layer in the bottom for "magnetic flux" using underbrace.

Here is what I have so far,

$$

 overbrace{ underbrace{S^1_A times  S^1_B}_{E} times  underbrace{S^1_C times  mathbb{R}}_{mathbb{CP}^{N-1}}

 }^{text{ABCDEFG}} 

$$

and my output is this:

Could you find a better way to do it? Effectively, how to do "Underbrace" under two "Underbraces"? Or maybe we can also try to use TikZ instead? (i.e. I don't mind to try other methods)

p.s. Another thing is that, in my case, the size of ABCDEFG is smaller than the S^1_A times S^1_B times S^1_C times mathbb{R} — is there a way to adjust the size of ABCDEFG and others?

Thank you for your help!!!

documentclass{article}

usepackage{mathtools,amssymb}

begin{document}



begin{gather*}

overbrace{underbrace{S^1_A times S^1_B}_Etimes

           underbrace{S^1_Ctimesmathbb{R}}_{mathbb{CP}^{N-1}}}^{text{ABCDEFG}} \[-normalbaselineskip]

underbrace{kern5em}_{text{magnetic flux}}

end{gather*}



end{document}

Solution 1: adjust by hand.

documentclass{article}

usepackage{amsfonts}

usepackage{mathtools}

begin{document}

[

 overbrace{ underbrace{S^1_A times  S^1_B}_{E} 

 makebox[7pt][c]{$underbrace{qquad~times~qquadvphantom{underbrace{S^1_C times  mathbb{R}}_{mathbb{CP}^{N-1}}}}_{text{magnetic flux}}$}

 underbrace{S^1_C times  mathbb{R}}_{mathbb{CP}^{N-1}}

 }^{text{ABCDEFG}} 

]

end{document}

Solution 2: TikZ.

documentclass{article}

usepackage{amsfonts,amsmath}

usepackage{tikz}

usetikzlibrary{tikzmark,decorations.pathreplacing}

begin{document}

[

 tikzmarknode{l}{S^1_A times  S^1_B}

 times

 tikzmarknode{r}{S^1_C times  mathbb{R}}

]

begin{tikzpicture}[overlay,remember picture,decoration={brace,raise=2pt},thick]

draw[decorate] (l.north west) -- (r.north east) node[midway,above=3pt](ABC){ABCDEFG};

draw[decorate] (l.south east) -- (l.south west) node[midway,below=3pt](E){$E$};

draw[decorate] (r.south east) -- (r.south west) node[midway,below=3pt](CP){$mathbb{CP}^{N-1}$};

draw[decorate] (CP.south east) -- (E.south west|-CP.south) node[midway,below=3pt]{magnetic flux};

end{tikzpicture}

end{document}

Solution 4 (or 5): measuring boxes

I decided to create a slightly more basic version of the solution below.

The macro bracetree, which I define below, creates the output you desire.
It does does this by putting some of its arguments in box registers so that their widths can be measured.
It then uses these width to insert the right amount of space at the right places to create braces with the correct widths

documentclass{article}



usepackage{amsmath}   %% <- not explicitly needed

usepackage{amsfonts}  %% <- for mathbb

usepackage{mathtools} %% <- for mathrlap, loads amsmath



makeatletter   %% <_ make @ usable in macro names

newcommand*bracetree[6]{%

  begingroup                           %% <- limit scope of assignments

    sbox0{$m@thdisplaystyle #1$}     %% <- store arguments in box registers

    sbox2{$m@th #4$}

    sbox4{$m@thdisplaystyle #3$}

    sbox6{$m@th #5$}

    hspace{dimexpr.5wd0-.5wd2}      %% <- insert space

    underbrace{

      hspace{dimexpr-.5wd0+.5wd2}   %% <- remove space

        underbrace{copy0}_{copy2}

          #2

        underbrace{copy4}_{copy6}    %% <- remove space

      hspace{dimexpr-.5wd4+.5wd6}

    }_{textstyle #6}

    hspace{dimexpr.5wd4-.5wd6}      %% <- insert space

  endgroup

}

makeatother    %% <- revert @



begin{document}



noindent Words before

begin{equation}

    overbrace{

      bracetree{S^1_A times  S^1_B}{times}{S^1_C times  mathbb{R}}

                {E}{mathbb{CP}^{mathrlap{N-1}}}

                {textnormal{magnetic fluxxxx}

      }

    }^{textstyletextnormal{ABCDEFG}}

end{equation}

Words after



end{document}

A few notes:

• ABCDEFG was smaller because the text above the overbrace is effectively like a superscript, and therefore set at the corresponding font size.
  This can be remedied by adding textstyle.
  I'm using textnormal instead of text because of the reasons outlined here.




• I'm using positive and negative hspaces that cancel out precisely to set the width of the bottom underbrace.




• I'm using mathrlap from mathtools to negate the horizontal space taken up by {N-1} because I think it looks better if the superscript is ignored for the purposes of brace placement and placement relative to braces.




• sbox<box register>{<contents>} stores <contents> in a box register. These boxes can be printed with copy<box register> and their widths are given by wd<box register>.
  I'm using only even box registers because these are available as scratch registers.




• m@th sets mathsurround (amount of horizontal space $…$) to zero. This is the default value, so it actually does nothing here. If you get rid of it you can also remove makeatletter and `makeatother.

Solution 3 (or 4): black magic

I made the version of bracetree below earlier by sort of taking apart the definition of the original underbrace. The results should mostly be the same, but it is a little harder to explain how this works (and probably for you to adapt).

documentclass{article}



usepackage{amsmath}   %% <- not explicitly needed

usepackage{amsfonts}  %% <- for mathbb

usepackage{mathtools} %% <- for mathrlap, loads amsmath



makeatletter %% <- make @ usable in macro names

newcommandbracetree[6]{%

  vtop{m@th

    sbox0{$mathstrutdisplaystyle #1$}%

    sbox2{$mathstrutdisplaystyle #3$}%

    sbox4{$mathstrut #4$}%

    sbox6{$mathstrut #5$}%

    ialign{##crcr

      $displaystylecopy0#2copy2$%

      crcr

      noalign{kern3p@nointerlineskip}%

      hbox to wd0{upbracefill}hfilhbox to wd2{upbracefill}%

      crcr

      hskip.5wd0hskip-.5wd4copy4hfilcopy6hskip-.5wd6hskip.5wd2

      crcr

      noalign{kern3p@nointerlineskip}%

      hskip.5wd0hskip-.5wd4upbracefillhskip-.5wd6hskip.5wd2

      crcr

      hskip.5wd0hskip-.5wd4hidewidthhbox{$#6$}hidewidthhskip-.5wd6hskip.5wd2

      crcr

      }%

  }%

}

makeatother  %% <- revert @



begin{document}



noindent Words before.

begin{equation}

    X = overbrace{

          bracetree{S^1_A times S^1_B}{times}{S^1_C times mathbb{R}}

                    {E}{mathbb{CP}^{mathrlap{N-1}}}

                    {text{magnetic flux}}

        }^{textstyletext{ABCDEFG}}

end{equation}

Words after.



end{document}

I'm not really sure where to begin explaining this, but here it goes.

• 
  vtop creates a top aligned box: the first line of its contents will share a baseline with the surrounding equation. See here.


• 
  ialign is sort of like tabular: it allows you to align things next to each other or on top of each other.


• 
  crcr more or less does what \ does in a tabular environment


• 
  noalign{kern<length>} inserts a little vertical space


• 
  hskip<length> inserts horizontal space


• 
  hfil and hidewidth both insert a stretchable amount of space. The latter will be negative when necessary.


• 
  upbracefill fills the available space with an underbrace

Solution 2.5: Tikz again

I've modified marmot's answer (with his blessing).
The difference between this version and his version is that this increases the depth of the equation (so "Words after" is actually below "magnetic flux").

DISCLAIMER: This nests TikZ environments!

Nesting TikZ environments is generally a bad idea because things like key values and bounding boxes can leak from the inner environment to the outer one and vice versa.
While marmot believes it should be okay in this case, one should still be careful with this.
See e.g this question and several pages linked to from there for more info.

If a modified version of this code is used elsewhere it is not guaranteed to still work smoothly.

documentclass{article}



usepackage{amsfonts,amsmath}

usepackage{tikz}

usetikzlibrary{tikzmark,decorations.pathreplacing}



begin{document}



noindent Words before

begin{equation}

    X = begin{tikzpicture}[baseline,remember picture,decoration={brace,raise=2pt},thick]

        node[anchor=base] {$tikzmarknode{l}{S^1_A times  S^1_B} times tikzmarknode{r}{S^1_C times  mathbb{R}}$};

        draw[decorate] (l.north west) -- (r.north east) node[midway,above=3pt](ABC){ABCDEFG};

        draw[decorate] (l.south east) -- (l.south west) node[midway,below=3pt](E){$strut Evphantom{^{N}}$};

        draw[decorate] (r.south east) -- (r.south west) node[midway,below=3pt](CP){$mathbb{CP}^{N-1}$};

        draw[decorate] (CP.south east) -- (E.south west|-CP.south) node[midway,below=3pt]{magnetic flux};

    end{tikzpicture}

end{equation}

Words after



end{document}