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Traces, lengths, axes and commensurability

Alan W. Reid (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

The focus of this paper are questions related to how various geometric and analytical properties of hyperbolic 3-manifolds determine the commensurability class of such manifolds. The paper is for the large part a survey of recent work.

Tropical intersection products on smooth varieties

Lars Allermann (2012)

Journal of the European Mathematical Society

We define an intersection product of tropical cycles on tropical linear spaces L k n , i.e. on tropical fans of the type max { 0 , x 1 , ... , x n } n - k · n . Afterwards we use this result to obtain an intersection product of cycles on every smooth tropical variety, i.e. on every tropical variety that arises from gluing such tropical linear spaces. In contrast to classical algebraic geometry these products always yield well-defined cycles, not cycle classes only. Using these intersection products we are able to define the pull-back...

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