Index
L, R, operators associated with
D2,
20
Rs,t,u(λ), see resolvent functions, 57
T
(n),
20
[·, ·]±, graded commutator, 56
A, a ∗-algebra, 33
B1(D, p), algebra of integrable elements , 13
B1
k(D,
p), smooth version of B1(D, p), 21
B2(D, p), algebra of square integrable
elements, 8
B2
k(D,
p), smooth version of B2(D, p), 21
D, a self-adjoint operator, 7
Du =
D|D|−u,
the deformation from D to
F =
D|D|−1,
57
H, a Hilbert space, 20
K(N , τ), KN , the τ-compact operators in
N , 33
Lp,
˜p,
L Schatten ideals, 9
Pn, seminorms on B1(D, p), 13, 14
Pn,l, seminorms on B1
k(D,
p) and
B1
∞(D,
p), 21
Φr
m,t
, see transgression cochain, 58
ΨM,u,
r
auxiliary cochain, 59
Qn, seminorms on B2(D, p), 8
α(k), combinatorial factors in index
formula, 56
•, parity notation, 55
N , a semifinite von Neumann algebra, 7
δ, δ , derivations associated with D, 20
δ-ϕ-topology, 46
δ-topology, 45
ηm, constant in the definition of the
resolvent cocycle, 58
λ-trick, 61
. . . m,r,s,t, expectation in the resolvent
cocycle, 58
. . . m,r,s,t, expectation in the
transgression cochain, 58
Z2-grading, 34
Om, functions holomorphic for
(z) (1 m)/2, 64
φm,
r
φm,t,
r
see resolvent cocycle, 58
φm, residue cocycle, 57
σn,l, combinatorial factors in index
formula, 56
σz,
the one parameter group associated to
D2,
23
τ, a faithful, semifinite, normal trace on a
von Neumann algebra, 7
τj , residue functionals, 56
ϕs, weights defined by D, 8
ζb(z), zeta functions in index formula, 56
du = [Du, ·], 57
s-trick, 61
OPr,
regular pseudodifferential operators
of order r, 22
OP0,
r
tame pseudodifferential operators of
order r, 22
deg, grading degree for operators, 55
dom(ϕs), domain of the weight ϕs, 8
dom(ϕs)1/2, ‘L2-domain’ of the weight ϕs,
8
Auxiliary cochain, 59
Bott projector, 41, 86
Bounded geometry, 91
Chern character, 50
Clifford bundle, 89
Conditional trace, 49
Covering space, 98
Cyclic cohomology, 48
(b, B)-cocycle, 49
cyclic cocycle, 48
normalised cocycle, 48
reduced (b, B)-cocycle, 49
Dirac bundle, 89
Dirac-type operator, 89
Discrete dimension spectrum, 56
Double construction, 39
Fatou Lemma, 10
Fredholm module, 37
Index pairing, 37
K-theoretical , 37
129
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