Symbol for contraction / interior product?

MnSymbol package has \invneg symbol, which is most likely what you're looking for. Hope this helps.

\documentclass{article}
\usepackage{mnsymbol}

\begin{document}
\[\invneg\]
\end{document}

Load the package MnSymbol in the preamble at the top of your tex file:

\usepackage{MnSymbol}

then in your body you can use:

\righthalfcup

See http://ctan.sharelatex.com/tex-archive/info/symbols/comprehensive/symbols-a4.pdf for more

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