• Title, Summary, Keyword: Anosov maps

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INFRA-NILMANIFOLDS AND THEIR FUNDAMENTAL GROUPS

  • Dekimpe, Karel;Igodt, Paul;Malfait, Wim
    • Journal of the Korean Mathematical Society
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    • v.38 no.5
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    • pp.883-914
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    • 2001
  • 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.

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