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"New Keywords: Migration and Borders" is a collaborative writing project aimed at developing a nexus of terms and concepts that fill-out the contemporary problematic of migration. It moves beyond traditional and critical migration studies by building on cultural studies and post-colonial analyses, and by drawing on a diverse set of longstanding author engagements with migrant movements. The paper is organized in four parts (i)

The research hypothesis that we call border as method offers a fertile ground upon which to test the potentiality and the limits of the topological approach. In this article we present our hypothesis and address three questions relevant for topology. First, we ask how the topological approach can be applied within the heterogeneous space of globalization, which we argue does not obey the dialectic of inclusion and exclusion. Second, we address the claim of neutrality that is often linked to the topological approach. Our point is that in mapping a space of flows and porous borders, the topological approach must be grasped in its ambivalence; it can become a tool for control as well as a tool for the expansion of freedom and equality. Finally, we argue that it is useful, perhaps even necessary, to locate the topological approach on the border, investigating concrete practices of border crossing that challenge the very possibility of a neutral mapping.