Some Constructions Involving Surgery on Surfaces in 4-manifolds
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This dissertation concerns embedded surfaces in smooth 4-manifolds and especially surgery on those surfaces. These cut and paste operations are a powerful tool in the study of smooth 4-manifolds, and we study these operations in several new contexts. We give applications to several different areas of low-dimensional topology, including embedding 3-manifolds into 4-manifolds, broken Lefschetz fibrations, slice knots, and the relationship between knots and 2-knots.