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Tables of Contents for Elliptic Genera and Vertex Operator Super-Algebras
Chapter/Section Title
Page #
Page Count
Introduction and summary of results.
1
378
Towards the signature of loop spaces: Elliptic genus
1
3
Elliptic genera
4
3
Vertex operator super-algebras
7
2
G-invariant vertex operator super-subalgebras and their vertex operators
9
4
Classifying spaces of geometric structures on manifolds
13
3
Elliptic genera as modules over vertex operator superalgebras
16
1
Infinite dimensional symmetries of elliptic genera for Kahler manifolds
17
5
Elliptic genera
22
27
Elliptic genera
22
7
Theta functions and elliptic functions
29
3
Proof of Theorem 4 of §1.1
32
3
The modular properties of elliptic genera
35
7
On the divisibility of coefficients of the elliptic genus ϕRell
42
4
Spinors on loop spaces: the Witten genus
46
3
Vertex operator super-algebras
49
44
Vertex operator super-algebras: A brief introduction
49
11
The infinite dimensional Clifford modules as vertex operator super-algebras and their modules
60
5
Clifford algebras, Virasoro algebras and affine Lie algebras as subalgebras of the vertex operator super-algebra V
65
7
The adjoint operators of vertex operators
72
21
G-invariant vertex operator super-subalgebras
93
129
VG as vertex operator super-algebra
93
1
Lie algebras as Lie subalgebras of Clifford algebras
94
10
Commutants of Lie subalgebras in o (2N) and Casimir elements
104
7
Generating G-invariant vectors in (V)
111
11
Vertex operators associated to G-invariant vectors of low weight
122
7
Unitary Virasoro algebras
129
10
Vertex operators generated by complex volume forms
139
8
Symplectic Virasoro algebras
147
27
Kahler forms in quaternionic vector spaces
174
11
Unitary Virasoro algebras in quanternionic vector spaces
185
3
Vertex operators for products of Kahler forms and their commutators
188
23
Determination of G-invariant vectors of low weight in the vertex operator super-algebra (V)
211
11
Geometric structures in vector spaces and reductions of structure groups on manifolds
222
81
Some geometric structures in vector spaces
222
14
Moduli of geometric structures as G-orbits in representation spaces: Some examples of interest
236
14
A general theory of geometric structures in vector spaces and their compatibilities
250
18
On connections and parallelism
268
17
Reductions of structure groups on manifolds and parallel sections
285
18
Infinite dimensional symmetries in elliptic genera for Kahler manifolds
303
76
Kahlerian manifolds
303
10
Generalizatios of Riemannian metrics, Riemannian volume forms, Kahler forms, complex volume forms, and quaternion-Kahler forms
313
13
Twisted G-Dirac operators
326
11
Elliptic genera as modules over vertex operator superalgebras of parallel sections
337
20
Infinite dimensional symmetries in elliptic genera for Kahler manifolds
357
22
References
379
4
Index of Notation
383
4
Subject Index
387