130 INDEX
numerical , 41
Index theorem
L2-index
theorem, 98, 101
Atiyah-Singer formula, 97, 98
Injectivity radius, 90
Isolated spectral dimension, 56
Jordan decomposition, 10, 16
Kasparov module, 35
local index formula, 83
McKean-Singer, 85
Moyal plane, 110
Projective tensor product, 11
Pseudodifferential operators, 22
regular, 22
tame, 22
Taylor expansion, 26
Residue cocycle, 57
Resolvent cocycle, 58
φm
r
defined using resolvent function
Rs(λ), 58
φm,t
r
defined using resolvent function
Rs,t(λ), 58
Resolvent function, 30, 57
Rs(λ) = (1 +
s2
+
D2))−1,
57
Rs,t,u(λ) = (t +
s2
+
Du))−1, 2
57
Rs,t(λ) = (t +
s2
+
D2))−1,
57
Schatten ideals, 9
Schatten norm estimates, 29
Semifinite Fredholm module, 37
finitely summable, 37
pre-Fredholm module, 37
Semifinite spectral triple, 34
QC∞, 45
QCk,
45
QCk
summable, 46
δ-ϕ-topology, 46
δ-topology, 45
discrete dimension spectrum, 56
finitely summable, 43
isolated spectral dimension, 56
smoothly summable, 46
spectral dimension, 43
Seminorms, 8
Pn, seminorms on B1(D, p), 13, 14
Pn,l, seminorms on B1
k(D,
p), B1
∞(D,
p),
21
Pr
n,l
, seminorms on OP0,
r
22
Qn, seminorms on B2(D, p), 8
Spectral dimension, 43
Torus actions, 103
Transgression cochain, 58
BΦM+1,0,u
r
defined using resolvent
function Rs,0,u(λ), 58
Φm,t
r
defined using resolvent function
Rs,t(λ), 58
Φm
r
defined using resolvent function
Rs(λ), 58
Weyl pseudodifferential calculus, 111
Zeta function, 56
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