%% Template for writing an Oberwolfach Report
%% maintained by <reports at mfo dot de>

%% Before submitting the report to <reports at mfo dot de>
%% you can run automated tests for common errors online at
%% http://www.mfo.de/scientific-programme/publications/owr/diagnostics

\documentclass[report]{owrart}

%% Enter additionally required packages below this comment.
%% * Please be conservative and only require common packages.
%% * Do not use any packages, which alter the page/font layout.
%% * For the inclusion of graphics, use the graphicx package.
%% * Please use .eps graphics only (no .jpg, .png or .pdf).
%% Note that the tex source has to be compilable to .dvi format.

\usepackage{hyperref}



%% The following are report-specific settings.
%% Usually, they do not need modification.
\reporter{Vassily Olegovich Manturov}  % Reporter of this report
\reportyear{2014} % The year of the report
\reportnumber{26} % The number of the report
\reportname{Algebraic Structures in Low-Dimensional Topology} % The title of the workshop
\reportdate{25 May -- 31 May 2014} % Date of the workshop
\organizers{Louis Hirsch Kauffman, Chicago\\Vassily Olegovich Manturov, Moscow\\Kent E. Orr, Bloomington\\Robert Schneiderman, New York} % Organizers
%% Example:
%% \reporter{Bill E. Xample}
%% \reportyear{2009}
%% \reportnumber{01}
%% \reportname{Algebraic Structures in Low-Dimensional Topology (Header)}
%% \reportdate{1 March -- 6 March 2005}
%% \organizers{Bill E. Xample, New York\Max Muster, M\"unchen}
%% Note: The number of the report differs from
%% the number of the workshop, which is 1422a.



%% The following settings may need modification:

%% Please insert an Mathematical Subject Classification (MSC)
%% of this report, eg: \subjclass{14xx, 27xx}
\subjclass{}

%% By default, the MSC is preceeded by
%% "Mathematics Subject Classification (2010)"
%% You can change this text with the following line:
%% \def\owrsubjclassname{Mathematics Subject Classification (2010)}

%% The default prefix 'Reporter:' displayed at the end of the report
%% in front of the reporter name can be changed, e.g. if there are two reporters
%% \reporterprefix{Reporters:}

%% By default, the title specified by \reportname is displayed also in
%% the header, on the title page and in the table of contents. In some
%% cases this is not convenient, and these settings can be altered by
%% the commands \reporthead, \reporttitle, and \reporttoc, respectively.
%% \reporthead{Algebraic Structures in Low-Dimensional Topology (Header)}
%% \reporttitle{Algebraic Structures in Low-Dimensional Topology (Title page)}
%% \reporttoc{Algebraic Structures in Low-Dimensional Topology (Toc)}

%% If the event was NOT a standard Oberwolfach Workshop,
%% please remove the comment and specify the type here.
%% eg: \workshoptype{Mini-Workshop}
%% \workshoptype{Workshop}

%% After every \begin{talk}, the command \resetcounters is called, which resets
%% the following counters: section, subsection, equation, footnote, figure.
%% If you want to automatically reset other counters as well (eg theorem),
%% you need to redefine this command as shown below.

%%\renewcommand{\resetcounters}{
%% \setcounter{section}{0}
%% \setcounter{subsection}{0}
%% \setcounter{equation}{0}
%% \setcounter{footnote}{0}
%% \setcounter{figure}{0}
%% \setcounter{theorem}{0}
%% \setcounter{definition}{0}
%%}

%% --------------------------------------------------------------------------
%% Enter own definitions (such as \newcommands and custom environments) here.
%% Please try to avoid using "\def" or "\renewcommand" as they may cause
%% interference among contributions of the authors.



\begin{document}

\begin{abstract}
%% Replace by own abstract, of course :-)

\noindent
Invariants of topological spaces of dimension three play a major role
in many areas, in particular \dots
\end{abstract}

\maketitle

\begin{introduction}
%% Feel free to begin with your own wording, of course :-)

\noindent
The workshop \emph{Invariants of topological spaces of dimension three},
organised by Max Muster (M\"unchen) and Bill E.~Xample (New York)
was well attended with over 30 participants with broad geographic
representation from all continents. This workshop was a nice blend of
researchers with various backgrounds \dots
\end{introduction}

\tableofcontents

\begin{report}

%% --------------------------------------------------------------------------
%% Please use the environment "talk" for each abstract.
%% It has three obligatory and one optional argument. The syntax is:
%% -----------------------
%% \begin{talk}[coauthors]{Name of the speaker}{Title of the talk}{Author Sorting Index}
%%      .....
%% \end{talk}
%% -----------------------
%% The names of coauthors will appear in form of "(joint work with ...)"
%%
%% The Author Sorting Index should be given as the last and first name of the speaker,
%% separated by a comma. If for example the name of the speaker is "John Smith", then
%% the correct Author Sorting Index is "Smith, John".
%% Any special characters (like accents, German umlaute, etc.) should be replaced by
%% their "non-special" version, eg replace \"a by a, \'a by a, etc.
%%
%% Please use the standard thebibliography environment to include
%% your references, and try to use labels for the bibitems, which
%% are uniquely assigned to you in order to avoid conflicts with other authors.
%% -------------------------------------------------------------------------------

\begin{talk}{Dror Bar-Natan}
{Some very good formulas for the Alexander polynomial}
{Bar-Natan, Dror}

\noindent
I will describe some very good formulas for a (matrix plus scalar)-valued extension of the Alexander polynnomial to tangles, then say that everything extends to virtual tangles, then roughly to simply knotted balloons and hoops in 4D, then the target space extends to (free Lie algebras plus cyclic words), and the result is a universal finite type of the knotted objects in its domain. Taking a cue from the BF topological quantum field theory, everything should extend (with some modifications) to arbitrary codimension-2 knots in arbitrary dimension and in particular, to arbitrary 2-knots in 4D. But what is really going on is still a mystery. 

My talk's handout, video, and further links are at \url{http://www.math.toronto.edu/~drorbn/Talks/Oberwolfach-1405/}.

\end{talk}

%% -------------------------------------------------------------------------------
%% If a talk was given by two authors, then you should use
%% the star version of the talk environment, which does not
%% add the speakers to the author index and does not make entries
%% into the table of contents. Syntax:
%% -----------------------
%% \begin{talk*}[coauthors]{Names of the speakers}{Title of the talk}
%%      .....
%% \end{talk*}
%% -----------------------
%%
%% The names of the authors have to be added by hand to the
%% author index by using the commands:
%% -----------------------
%% \aindex{1st Author Sorting Index}{Name of 1st Author}
%% \aindex{2nd Author Sorting Index}{Name of 2nd Author}
%% ...
%% -----------------------
%%
%% Furthermore, the entry for the table of contents has to
%% be created manually by
%% \mtitem{Author Name(s) (joint with coauthors)}{Title of the talk}
%% -------------------------------------------------------------------------------

\begin{talk*}{Max M\"uller, Peter Mustermann}
{Computing other invariants of topological spaces of dimension three}

\aindex{Muller, Max}{Max M\"uller}
\aindex{Mustermann, Peter}{Peter Mustermann}

\mtitem{Max M\"uller, Peter Mustermann}
{Computing other invariants of topological spaces of dimension three}

\noindent
The computation of ...

\end{talk*}

\end{report}

%% -------------------------------------------------
%% The list of e-mail and postal addresses of the participants will be
%% inserted by the administration of MFO after your submission of
%% this file to "reports at mfo dot de".
%% -------------------------------------------------

\end{document}