Toroidal Groups Book

	Introduction	1
1	The Concept of Toroidal Groups	3
1.1	Irrationality and toroidal coordinates	3
	Toroidal groups	3
	Complex homomorphisms	7
	Toroidal coordinates and C[superscript n-q]-fibre bundles	9
	Maximal Stein subgroups of toroidal groups	14
1.2	Toroidal subgroups and pseudoconvexity	16
	The maximal toroidal subgroup of a complex Lie group	16
	Pseudoconvexity	19
	The maximal complex subtorus of a complex Lie group	22
2	Line Bundles and Cohomology	25
2.1	Line bundles on toroidal groups	25
	Automorphic factors	25
	The characteristic decomposition of an exponential system	28
	Automorphic summands	32
	Theta bundles and topologically trivial line bundles	37
2.2	Cohomology of toroidal groups	44
	Toroidal theta and wild groups	44
	Dolbeault cohomology of toroidal theta groups	47
	Dolbeault cohomology of complex Lie groups	54
3	Quasi-Abelian Varieties	57
3.1	Ample Riemann forms	57
	The Hermitian decomposition of an automorphic factor	57
	Period relations	61
	Ample Riemann forms	64
	Maximal Stein subgroups of quasi-Abelian varieties	68
3.2	Characterization of quasi-Abelian varieties	73
	Cohomology and the average of differential forms	73
	Chern forms of fibre metrics	80
	Holomorphic mappings to projective spaces	85
	Meromorphic functions on toroidal groups	88
4	Reduction and Extension	93
4.1	Automorphic forms	93
	Reduction to the positive definite case	93
	Further properties of meromorphic functions	101
	Existence of automorphic forms and Lefschetz type theorems	103
4.2	Extendable line bundles	106
	The case of C[superscript n-q]-fibre bundles	106
	The case of kind l	113
	Explicit representation of automorphic forms	120
	References	125
	Index	131