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

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.

See also

• L² cohomology

References

• Baily, Walter L. Jr.; Borel, Armand (1964), "On the compactification of arithmetically defined quotients of bounded symmetric domains", Bulletin of the American Mathematical Society, 70 (4): 588–593, doi:10.1090/S0002-9904-1964-11207-6, MR 0168802
• Baily, W.L.; Borel, A. (1966), "Compactification of arithmetic quotients of bounded symmetric domains", Annals of Mathematics, 2, Annals of Mathematics, 84 (3): 442–528, doi:10.2307/1970457, JSTOR 1970457, MR 0216035
• Gordon, B. Brent (2001) [1994], "Baily–Borel compactification", Encyclopedia of Mathematics, EMS Press