mathematics

Robion Kirby

Robion Kirby is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Robion Kirby rather than just read about it. In short: Robion Cromwell Kirby (born February 25, 1938) is a Professor of Mathematics at the University of California, Berkeley who specializes in low-dimensional topology. Together with Laurent C.

Key takeaways

Robion Kirby belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Robion Kirby to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Robion Kirby from memory before moving on to harder problems.

Reference excerpt

Robion Cromwell Kirby (born February 25, 1938) is a Professor of Mathematics at the University of California, Berkeley who specializes in low-dimensional topology. Together with Laurent C. Siebenmann he developed the Kirby–Siebenmann invariant for classifying the piecewise linear structures on a topological manifold. He also proved the fundamental result on the Kirby calculus, a method for describing 3-manifolds and smooth 4-manifolds by surgery on framed links. Along with his significant mathematical contributions, he has over 50 doctoral students and is the editor of an influential problem list.

Career He received his Ph.D. from the University of Chicago in 1965, with thesis "Smoothing Locally Flat Imbeddings" written under the direction of Eldon Dyer. He soon became an assistant professor at UCLA. While there he developed his "torus trick" which enabled him to solve, in dimensions greater than four (with additional joint work with Siebenmann), four of John Milnor's seven most important problems in geometric topology. In 1971, he was awarded the Oswald Veblen Prize in Geometry by the American Mathematical Society. In 1995 he became the first mathematician to receive the NAS Award for Scientific Reviewing from the National Academy of Sciences for his problem list in low-dimensional topology. He was elected to the National Academy of Sciences in 2001. In 2012 he became a fellow of the American Mathematical Society. Kirby is also the President of Mathematical Sciences Publishers, a small non-profit academic publishing house that focuses on mathematics and engineering journals.

Books Kirby, Robion C.; Siebenmann, Laurence C. (1977). Foundational Essays on Topological Manifolds, Smoothings, and Triangulations (PDF). Annals of Mathematics Studies. Vol. 88. Princeton, NJ: Princeton University Press. ISBN 0-691-08191-3. MR 0645390. Kirby, Robion C. (1989). The Topology of 4-Manifolds. Lecture Notes in Mathematics. Vol. 1374. Berlin, New York: Springer-Verlag. doi:10.1007/BFb0089031. ISBN 978-3-540-51148-9. MR 1001966.

References

External links Kirby's home page. Biographical notes Archived 2011-08-07 at the Wayback Machine from the Proceedings of the Kirbyfest in honour of his 60th birthday in 1998. Video Lectures by Kirby at Edinburgh

Illustrations

Worked examples

Example 1 — a first encounter with Robion Kirby

Start with the simplest possible case. Write down what Robion Kirby claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Robion Kirby before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Robion Kirby ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Robion Kirby

In research: Robion Kirby appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Robion Kirby in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Robion Kirby is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1938 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Robion Kirby outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Robion Kirby in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Robion Kirby means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Robion Kirby out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Robion Kirby in simple terms?

Robion Cromwell Kirby (born February 25, 1938) is a Professor of Mathematics at the University of California, Berkeley who specializes in low-dimensional topology. Together with Laurent C.

Why does Robion Kirby matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Robion Kirby?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Robion Kirby.