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Actual problems of noncommutative geometry and topology
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. . 10 100 , ([2], [3], [4]).


1998­2001 . . . . [5] , [6] [7]. . . [8] , . , , , . , , (), () . . [5] , . . . . . [9, 10] , , . . . , .. , , . , . , . , . . ([11]) .

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. , , , , . . . . ([12], [13]) ([13]) H (g) , g: signH(L) = signE2 p,q E2 - E2 = Hp q (M ; Hq (g)) . ([14]), . . . ([15],[16]) , ([17]). . , , .

C -
C - [18, 19, 20] - C - . , C - , . [21] l2 , .. , C -. , , . - , , K - K (X ; A) " C - A", , A ( ) C - ( ) . K - C - . , l2 (A) , , , (GL GL ) . , K -. , . , 1982 . . . . , , C - . 3


, , . - . . C . . [22] . C - . . . . , . l2 (A) , . . , , . . , , , C - [23]. C - . . , . . . [24] C -, . , , . . , , . , . , n, , n, . . . [25]. . . [26]. , , , C -, ( ) K - . . . . . [27, 28] . N0 ( W -) K -. K -. , N - W -. , N0 (A) C K0 (A)- W - . () N0 (A). , N0 (A) ( ) W - A, K0 (A) .

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[29] . . , K , , , , .. B (H ) H . , , [29], , C - A = C (K ) K . C -: , , , .. . , . C - [19] : , , , . , , , , . . . ([29]) , . . . . . [30] C -. , . , () . , .. , K - () . ( [19]) C - C (K ) K [29]. , , C (K ), . I M , I M C (K ).


, , , , , , , . , , , , , , . 5


. . , ( ), . , . , . . , , . [31] . C -, C - , , K1 - . . , , B , , в Z . , . [32] , K0 (B ) , K0 (B ). , : , . , , , (, ), . . . [33] () . , ( , ()), - (x) C ( ), 0 C . C - C - ­, C -. E -. E - , - , , . C - (. , . , . , . ) , . . . . [34, 35, 36, 37, 38, 39, 40, 41, 42] . [36] , . , , 6


C -, , , . C - [38] , , . C - . : (.. ­) . [39] , , .. (t )tR : C0 (R; A) B , t+s (f ) = t (s (f )), f C0 (R; A) C - A, s (f )(x) = f (x + s). [43], . . . . [41] . C -, , () . C - K0 - C - , , . C -, .. *-, . , , . [40]. [44] . , . , C - . [37], E - ­ K K - . , C - A B E (A, B ) = K K (A, Q(B )), Q(B ) B . [42] () C - . , . , ( K -). , --, .. K - C - . -- . C - , () . , "" . C -. . . [45] C - , . , 7


­ . , () .


, C -, . . . : , C -, , , , (" " C - ). , [46]. . . . , . [47, 48]. ( ), , : . . . . , : ^ ^ I [49]. [50]. [51, 52]. [53] --, , . . . [54] , , , , .


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