Baily–Borel compactification

In mathematics, the Baily–Borel compactification is a compactification of a quotient of a Hermitian symmetric space by an arithmetic group, introduced by W.L. Baily and A. 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, W.L.; Borel, A. (1964), "On the compactification of arithmetically defined quotients of bounded symmetric domains", Bull. Amer. Math. Soc., 70 (4): 588–593, doi:10.1090/S0002-9904-1964-11207-6 
• Baily, W.L.; Borel, A. (1966), "Compactification of arithmetic quotients of bounded symmetric domains", Ann. of Math. (2), Annals of Mathematics, 84 (3): 442–528, JSTOR 1970457, doi:10.2307/1970457 
• Gordon, B. Brent (2001) [1994], "B/b130010", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4