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Contact geometry
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==Applications== Like symplectic geometry, contact geometry has broad applications in [[physics]], e.g. [[geometrical optics]], [[classical mechanics]], [[thermodynamics]], [[geometric quantization]], [[Dispersionless equation#Multidimensional integrable dispersionless systems|integrable systems]] and to [[control theory]]. Contact geometry also has applications to [[low-dimensional topology]]; for example, it has been used by [[Kronheimer]] and [[Tomasz Mrowka|Mrowka]] to prove the [[property P conjecture]], by [[Michael Hutchings (mathematician)|Michael Hutchings]] to define an invariant of smooth three-manifolds, and by [[Lenhard Ng]] to define invariants of knots. It was also used by [[Yakov Eliashberg]] to derive a topological characterization of [[Stein manifold]]s of dimension at least six. Contact geometry has been used to describe the [[visual cortex]].<ref>{{Cite journal |last=Hoffman |first=William C. |date=1989-08-01 |title=The visual cortex is a contact bundle |url=https://www.sciencedirect.com/science/article/pii/009630038990091X |journal=Applied Mathematics and Computation |volume=32 |issue=2 |pages=137β167 |doi=10.1016/0096-3003(89)90091-X |issn=0096-3003|url-access=subscription }}</ref>
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