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Abstract: It has recently been shown that infinite matroids can be axiomatized in a waythat is very similar to finite matroids and permits duality. This waspreviously thought impossible, since finitary infinite matroids must havenon-finitary duals. In this paper we illustrate the new theory by exhibitingits implications for the cycle and bond matroids of infinite graphs. We alsodescribe their algebraic cycle matroids, those whose circuits are the finitecycles and double rays, and determine their duals. Finally, we give asufficient condition for a matroid to be representable in a sense adapted toinfinite matroids. Which graphic matroids are representable in this senseremains an open question.

Autor: Henning Bruhn, Reinhard Diestel


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