Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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INFRA-NILMANIFOLDS AND THEIR FUNDAMENTAL GROUPS

  • Dekimpe, Karel (Katholieke Universiteit Leuven, Campus Kortrijk, Belgium) ;
  • Igodt, Paul (Katholieke Universiteit Leuven, Campus Kortrijk, Belgium) ;
  • Malfait, Wim (Katholieke Universiteit Leuven, Campus Kortrijk, Belgium)
  • Published : 2001.09.01
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Abstract

We present a survey of research results obtained for infra-nilmanifolds, their fundamental groups and some of their generalizations. This is presented from two different approaches and covers achievements obtained during the past four decades and showing a remarkable amount of mathematical interdisciplinarity. We go more in depth concerning the existence and construction of polynomial structures for these manifolds and groups, a direction where significant progress was made in the past few years. The bounded-degree polynomial structures developed by the authors triggered a number of challenging open problems. Also, their study already has lead to some interesting results concerning e.g. Anosov diffeomorphisms and expanding maps.

Keywords

References

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