Baily–Borel compactification

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In mathematics, the Baily–Borel compactification is a compactification of a quotient of a Hermitean symmetric space by an arithmetic group, introduced by W.L. Baily and A. Borel (1964, 1966).

[edit] Example

• If C is the quotient of the upper half plane by a congruence subgroup of SL₂(Z), then the Baily–Borel compactification of C is formed by adding a finite number of cusps to it.

[edit] See also

• L2 cohomology

[edit] References

• Baily, W.L. & Borel, A. (1964), “On the compactification of arithmetically defined quotients of bounded symmetric domains”, Bull. Amer. Math. Soc. 70: 588–593, <http://www.ams.org/bull/1964-70-04/S0002-9904-1964-11207-6/> 
• Baily, W.L. & Borel, A. (1966), “Compactification of arithmetic quotients of bounded symmetric domains”, Ann. of Math. (2) 84: 442–528, <http://links.jstor.org/sici?sici=0003-486X%28196611%292%3A84%3A3%3C442%3ACOAQOB%3E2.0.CO%3B2-H> 
• Gordon, B. Brent (2001), “Baily–Borel compactification”, in Hazewinkel, Michiel, Encyclopaedia of Mathematics, Kluwer Academic Publishers, ISBN 978-1556080104