1 Introduction ................................................. 7
2 The cusp calculus ........................................... 10
2.1 Basic properties of cusp operators ..................... 16
2.2 The cusp Dirac operator ................................ 23
2.3 The even dimensional case .............................. 23
2.4 The odd dimensional case ............................... 24
3 Trace functionals ........................................... 25
3.1 The trace anomaly formula ............................... 31
4 A brief introduction to the BRST-formalism .................. 34
5 Descent equations in the finite dimensional case ............ 37
6 Forms associated with families of Dirac operators ........... 43
7 Eta-forms and localization: a first look .................... 46
7.1 Eta 1-form ............................................. 46
7.2 Eta 2-form ............................................. 47
7.3 Eta 3-form ............................................. 48
8 Regularization of the forms F(dF)m .......................... 49
9 Noncommutative BRST-complex ................................. 51
9.1 BRST-complex ........................................... 52
9.2 Superconnections ....................................... 55
9.3 The total superconnection .............................. 58
9.4 Superconnection character forms ........................ 59
9.5 The triangle formula ................................... 64
10 Eta-chains and eta-cocycles ................................. 70
10.1 Basic definitions ...................................... 70
10.2 Homotopy invariance of eta-cocycles .................... 73
10.3 Locality ............................................... 76
11 Decomposition theorems ...................................... 76
11.1 Superconnection  = tα + θ ............................. 77
11.2 The general case ....................................... 85
11.3 Superconnection = tθ ................................. 89
12 Further properties of eta-cocycles and computations ......... 94
12.1 Reducing eta-chains .................................... 94
13 A regularization of eta-cocycles ............................ 96
13.1 The counterterm regularization of Mickelsson and
Paycha ................................................. 98
14 Computations of eta-cocycles ................................ 99
14.1 Computations in the case = tθ ........................ 99
14.2 Computations in the case = tα + θ ................... 100
15 The odd case ............................................... 102
15.1 Local formulas ........................................ 105
15.2 Mickelsson-Faddeev-Shatasvili-cocycle ................. 105
15.3 Schwinger term in dimension 5 ......................... 107
15.4 The general Schwinger term ............................ 109
16 Zero modes ................................................. 112
16.1 The fully elliptic case ............................... 112
16.2 The general case ...................................... 113
17 Summary .................................................... 114
17.1 Open problems ......................................... 115
18 Appendix: Decomposing the forms F(dF)m ..................... 116
References .................................................... 119
| 
