How to create \Delta with dot in it?

Question

I am just looking for ways to write different \Delta´s (so many different variants of the Alexander polynomial).

So I came up with the idea to have a dot in it. But the problem I noticed is, if I write it like below: The dot moves around.

\documentclass{article}
\usepackage{amsmath,amssymb}
\newcommand*{\dotDelta}{\Delta\hspace{-0.61em}\boldsymbol{\cdot}}
\begin{document}
$\dotDelta a$

$\dotDelta$

$\dotDelta (k)=t^2$
\end{document}

Only the dot in the middle line remains at the right position.

Answer 1

I'd avoid bolding the dot.

\documentclass{article}

\makeatletter
\newcommand{\dotDelta}{{\vphantom{\Delta}\mathpalette\d@tD@lta\relax}}
\newcommand{\d@tD@lta}[2]{%
  \ooalign{\hidewidth$\m@th#1\mkern-1mu\cdot$\hidewidth\cr$\m@th#1\Delta$\cr}%
}
\makeatother

\begin{document}
$\dotDelta a$

$\dotDelta_{\dotDelta_{\dotDelta}}$

$\dotDelta (k)=t^2$
\end{document}

Changing the dot into the bold version just requires adding \boldmath at the appropriate spot:

\newcommand{\d@tD@lta}[2]{%
  \ooalign{\hidewidth\boldmath$\m@th#1\mkern-1mu\cdot$\hidewidth\cr$\m@th#1\Delta$\cr}%
}

See \subseteq + \circ as a single symbol ("open subset") for a quick course on \ooalign. The only trick here is moving the dot a bit to the left for compensating the thick strokes on the right of the Delta.