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Genus inequalities and four-dimensional surgery

By Ronnie Lee and Dariusz M. Wilczyński


AbstractWe obtain a new genus inequality for a topologically locally flat surface in a 4-dimensional manifold. This inequality provides new information about the fundamental group of the complement of such a surface and in many cases gives the minimum genus among surfaces within the same homology class. The general problem of finding an embedded surface of a small genus allowed by the inequality remains undecided and is directly related to the surgery conjecture of 4-dimensional topology

Publisher: Elsevier Science Ltd.
Year: 2000
DOI identifier: 10.1016/S0040-9383(99)00017-8
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