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# 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, doi:10.2307/1970457, JSTOR 1970457

Gordon, B. Brent (2001), "B/b130010", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4

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