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\ihead{Errata to ``Combinatorial Novikov-Morse theory''}
\ohead{\today}
\begin{document}

\begin{center}
\textbf{Combinatorial Novikov-Morse theory}

\textit{Robin Forman}

\url{https://math.rice.edu/~forman/novall.ps}

version of 1999

\textbf{Errata and addenda by Darij Grinberg}

\bigskip
\end{center}

\setcounter{section}{6}

\section{Errata and addenda}

The following list contains some corrections and comments to Robin Forman's
paper \textquotedblleft Combinatorial Novikov-Morse theory\textquotedblright.
I refer to the preprint version of 1999 of this paper (available from
\url{https://math.rice.edu/~forman/novall.ps} ), but some of the errors listed
below might also be contained in the published version.

I have only skimmed the first half of the paper, so the list below is probably
far from comprehensive, but I hope it is still of use.

\begin{itemize}
\item \textbf{page 3:} The \textquotedblleft$>$\textquotedblright\ sign after
\textquotedblleft Let $K$ denote the set of open cells of $M$%
\textquotedblright\ should be a period.

\item \textbf{page 3:} In the definition of a critical cell, replace
\textquotedblleft$f\left(  \gamma\right)  \leq f\left(  \alpha\right)
$\textquotedblright\ by \textquotedblleft$f\left(  \gamma\right)  \geq
f\left(  \alpha\right)  $\textquotedblright.

\item \textbf{page 5:} In the displayed equation%
\[
\#\left\{  \gamma^{\left(  p-1\right)  }<\alpha\mid\omega\left(  \gamma
>\alpha\right)  \leq0\right\}  =0,
\]
replace \textquotedblleft$\omega\left(  \gamma>\alpha\right)  $%
\textquotedblright\ by \textquotedblleft$\omega\left(  \alpha>\gamma\right)
$\textquotedblright.

\item \textbf{page 6:} The period at the end of the displayed equation
\[
\left\langle \partial_{t}\beta,\alpha\right\rangle =e^{t\omega\left(
\beta<\alpha\right)  }\left\langle \partial\beta,\alpha\right\rangle
\]
should be a comma.

\item \textbf{page 6:} In the last displayed equation of this page, replace
\textquotedblleft$\partial_{t}\partial_{t}^{\ast}\rightarrow\partial_{t}%
^{\ast}\partial_{t}$\textquotedblright\ by \textquotedblleft$\partial
_{t}\partial_{t}^{\ast}+\partial_{t}^{\ast}\partial_{t}$\textquotedblright.

\item \textbf{page 7:} \textquotedblleft has a limits\textquotedblright%
\ $\rightarrow$ \textquotedblleft has a limit\textquotedblright.

\item \textbf{page 11:} \textquotedblleft in which we must
work\textquotedblright\ $\rightarrow$ \textquotedblleft we must
work\textquotedblright.

\item \textbf{page 12:} In the complex just above Theorem 1.2, there is a
redundant parentheses \textquotedblleft$)$\textquotedblright.

\item \textbf{page 14:} \textquotedblleft which maps each\textquotedblright%
\ $\rightarrow$ \textquotedblleft which map each\textquotedblright.

\item \textbf{page 15:} \textquotedblleft which maps each\textquotedblright%
\ $\rightarrow$ \textquotedblleft which map each\textquotedblright.

\item \textbf{page 17:} \textquotedblleft for ant $F$\textquotedblright%
\ $\rightarrow$ \textquotedblleft for any $F$\textquotedblright.

\item \textbf{page 17:} On the very last line of this page, \textquotedblleft%
$\omega\left(  \alpha>\beta\right)  +\omega\left(  \beta>\alpha\right)
$\textquotedblright\ should be \textquotedblleft$\omega\left(  \alpha
>\beta\right)  +\omega\left(  \beta>\gamma\right)  $\textquotedblright.

\item \textbf{page 19:} Replace \textquotedblleft$\left[  \delta\right]
=H^{1}\left(  M,\mathbb{R}\right)  $\textquotedblright\ by \textquotedblleft%
$\left[  \delta\right]  \in H^{1}\left(  M,\mathbb{R}\right)  $%
\textquotedblright.

\item \textbf{page 20, Definition 2:} Replace \textquotedblleft%
2)\textquotedblright\ by \textquotedblleft(2)\textquotedblright.

\item \textbf{page 33:} \textquotedblleft$2x2$\textquotedblright%
\ $\rightarrow$ \textquotedblleft$2\times2$\textquotedblright.
\end{itemize}


\end{document}