= Mark Powell
{c}
<Mark Powell> studies the <topology> of manifolds, especially in dimensions three and four, together with <homological algebra>. His Glasgow profile verifies this research specialization.https://www.gla.ac.uk/schools/mathematicsstatistics/staff/markpowell/[Institutional research statement]{ref}
His <Introduction to Differential Geometry by Mark Powell> connects the local geometry of curves and surfaces with global invariants. <Curvature> and <torsion of a curve> describe how a curve bends in space, whereas the <Gauss-Bonnet theorem> turns integrated surface curvature and boundary terms into an <Euler characteristic>. These examples show how local differential measurements can constrain a whole geometric object.<Introduction to Differential Geometry by Mark Powell>[Part I, sections 2.1 and 2.5–2.8; Part VI, sections 7.1–7.5]{ref}
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