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 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, https://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", Annals of Mathematics, 2 (Annals of Mathematics) 84 (3): 442–528, doi:10.2307/1970457 
• Hazewinkel, Michiel, ed. (2001), "Baily–Borel compactification", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=Main_Page