Karoubi conjecture
{{short description|Theorem connecting algebraic and topological K-theories on C* algebras}}
In mathematics, the Karoubi conjecture is a conjecture by {{harvs|txt|authorlink=Max Karoubi|last=Karoubi|first=Max|year=1979}} that the algebraic and topological K-theories coincide on C* algebras spatially tensored with the algebra of compact operators. It was proved by {{harvs|txt|last1=Suslin|first1=Andrei|author1-link=Andrei Suslin|last2=Wodzicki|first2=Mariusz|author2-link=Mariusz Wodzicki|year1=1990|loc1=theorem 6|year2=1992}}.
References
- {{Citation | last1=Karoubi | first1=Max | author1-link=Max Karoubi|editor1-last=Harpe | editor1-first=Pierre de la | title=Algèbres d'opérateurs (Sém., Les Plans-sur-Bex, 1978) | publisher=Springer-Verlag | location=Berlin, New York | series=Lecture Notes in Mathematics | doi=10.1007/BFb0062621 | mr=548119 | year=1979 | volume=725 | chapter=K-théorie algébrique de certaines algèbres d'opérateurs | pages=254–290| isbn=978-3-540-09512-5 }}
- {{Citation | last1=Suslin | first1=Andrei A. | author1-link=Andrei Suslin| last2=Wodzicki | first2=Mariusz |author2-link=Mariusz Wodzicki| title=Excision in algebraic K-theory and Karoubi's conjecture | jstor=2356456 | mr=1081504 | year=1990 | journal=Proceedings of the National Academy of Sciences of the United States of America | issn=0027-8424 | volume=87 | issue=24 | pages=9582–9584 | doi=10.1073/pnas.87.24.9582| pmc=55216 | pmid=11607130| bibcode=1990PNAS...87.9582S | doi-access=free }}
- {{Citation | last1=Suslin | first1=Andrei A. | author1-link=Andrei Suslin| last2=Wodzicki | first2=Mariusz | author2-link=Mariusz Wodzicki| title=Excision in algebraic K-theory | doi=10.2307/2946546 | mr=1173926 | year=1992 | journal=Annals of Mathematics |series=Second Series | issn=0003-486X | volume=136 | issue=1 | pages=51–122| jstor=2946546 }}
Category:Theorems in algebraic topology
Category:Conjectures that have been proved
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