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{\Large המחלקה למתמטיקה, בן-גוריון}

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{\Huge תורת החבורות וגיאומטריה}\\[0.2\baselineskip]

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\textbf{ב}\emph{יום ראשון,  7 במאי, 2017}
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\textbf{בשעה} \emph{14:30 -- 15:30}
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\textbf{ב}\emph{-101}

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ההרצאה

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{\Large\bfseries Aut-invariant metrics and Aut-invariant quasimorphisms on free groups and surface groups.\par}
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תינתן על-ידי
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{\large\scshape Michal Marcinkowski}
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\textbf{תקציר:}
  **Lecture 2. **

There are two interesting norms on free groups and surface groups 
which are invariant under the group of all automorphisms:

A) For free groups we have the primitive norm, i.e., \textbar{}g\textbar{}\_p = the 
minimal number of primitive elements one has to multiply to get g.

B) For fundamental group of genus g surface we have the simple 
curves norm, i.e., \textbar{}g\textbar{}\_s = the minimal number of simple closed curves 
one need to concatenate to get g.

In our recent paper with M. Brandenbursky we prove the following dichotomy: either \textbar{}g\^{}n\textbar{} is 
bounded or growths linearly with n. For free groups and surface groups 
we give an explicit characterization of (un)bounded elements.

In two talks I will explain the idea of the proof and draw a number of 
consequences. The proof uses the theory of mapping class groups 
(i.e. Nielsen-Thurston normal form, Birman embedding) and 
quasimorphisms.
  


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