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
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, 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) (Annals of Mathematics) 84 (3): 442–528, doi:10.2307/1970457, JSTOR 1970457
- Gordon, B. Brent (2001), "Baily–Borel compactification", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1556080104, http://www.encyclopediaofmath.org/index.php?title=B/b130010