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In this publication a tropical intersection theory is established with analogue notions and tools as its algebrogeometric counterpart. The developed theory, interesting as a subfield of convex geometry on its own, shows many relations to the intersection theory of toric varieties and other fields. In the second chapter, tropical intersection theory is used to define and study tropical gravitational descendants (i.e. GromovWitten invariants with incidence and "Psiclass" factors). It turns out that many concepts of the classical GromovWitten theory such as the WDVV equations can be carried over to the tropical world.
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