Theodore Frankel

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Theodore Frankel (June 17, 1929 – August 5, 2017)[1] was a mathematician who introduced the Andreotti–Frankel theorem and the Frankel conjecture.

Frankel received his Ph.D. from the

relativity theory. He joined the UC San Diego mathematics department in 1965, after serving on the faculties at Stanford University and Brown University
.

Research

In the 1930s,

totally geodesic compact submanifolds must intersect if their dimensions are large enough. The idea is to apply Synge's method to a minimizing geodesic between the two submanifolds. By the same approach, Frankel proved that complex submanifolds of positively curved Kähler manifolds must intersect if their dimensions are sufficiently large. These results were later extended by Samuel Goldberg and Shoshichi Kobayashi to allow positivity of the holomorphic bisectional curvature.[3]

Inspired by work of

Given a

de Rham theorem applies to construct a function whose critical points coincide with the zeros of the vector field. A second-order analysis at the critical points shows that the set of zeros of the vector field is a nondegenerate critical manifold for the function. Following Raoul Bott's development of Morse theory for critical manifolds, Frankel was able to establish that the Betti numbers of the manifold are fully encoded by the Betti numbers of the critical manifolds, together with the index of his Morse function along these manifolds. These ideas of Frankel were later important for works of Michael Atiyah and Nigel Hitchin, among others.[5][6]

Major Publications

Articles

Textbooks

References