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Mathematicians marvel at 'crazy' cuts through four dimensions
Topologists prove two new results that bring some order to the confoundingly difficult study of four-dimensional shapes.
Their findings suggested that the members of a broad class of surfaces all slice through their parent manifold in a relatively simple way, leaving a fundamental property unchanged. In February, together with Daniel Ruberman of Brandeis University, Hughes constructed a sequence of counterexamples — “crazy” two-dimensional surfaces that dissect their parent manifolds in ways that mathematicians had believed to be impossible. Nevertheless, in March, İnanç Baykur of the University of Massachusetts, Amherst, who organized last year’s list-making conference with Ruberman, announced the solution to another problem involving simply connected four-dimensional manifolds from the 1997 list.
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