Topology of surface diagrams of smooth 4-manifolds.
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- Record sourced from PubMed, PMID 21518896.
- Also identified by DOI 10.1073/pnas.1016952108 and PMC identifier 3100938.
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Abstract
Surface diagrams are a new way to specify any smooth closed orientable 4-manifold by an orientable surface decorated with simple closed curves. These curves are cyclically indexed, and each curve has a unique transverse intersection with the next. The aim of this paper is to announce a uniqueness theorem for these objects (within a fixed homotopy class) that turns out to be similar to the Reidemeister-Singer theorem for Heegaard splittings of 3-manifolds.