Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Acknowledgements
Preface
Part 1: Classical theory of derivation
Chapter 1: Coordinate methods
1. Translation planes and quasifibrations
2. Quasifields
3. Left quasifields
4. T-extension
Chapter 2: Embedding theory of derivable nets
1. Co-dimension 2 construction
2. Structure theory and contraction of embedded nets
3. Embedding of subplane covered nets
4. Transversals to derivable nets
Part 2: Classifying derivable nets over skewfields
Chapter 3: Fundamentals & background
1. Uniform representation for quaternion division rings
2. Quaternion division ring planes
3. Matrices and determinants over skewfields
4. Classifying derivable nets
Chapter 4: Classification theory over skewfields
1. Notation
2. Extension of skewfields theorem/Skewfield bimodules
3. Preliminary types 1, 2, 3
4. Standard framework
5. Generalized quaternions over skewfields
6. Matrix skewfields are generalized quaternion
7. Generalized G(a, b)F contains (a, b)Z(F)
8. Artin-Wedderburn theorem & Brauer groups
9. Extending skewfields
Part 3: Types i of derivable nets
Chapter 5: The types
1. Type 0
2. Double regulus type 0 derivable nets
3. The ambient space
4. Derivable nets of type 3
5. Order in type 3 derivable nets
6. Derivable nets of type 2
7. Fake type 2 derivable nets
8. Open form derivable nets of type 2
9. Order in type 2 derivable nets
10. Derivable nets of type 1
11. Examples of type 1 derivable nets
12. Carrier nets
13. Derivable nets in translation planes
Part 4: Flocks of α-cones
Chapter 6: Klein quadric and generalization
1. α-Klein quadric
2. Construction of general flocks
3. The field case
4. Algebraic construction for α-cones
5. Elation groups and flokki planes
6. Maximal partial spreads and α-flokki
7. The second cone
8. Baer groups for flokki planes
9. q-Flokki and lifting
10. Collineations and isomorphisms of α-flokki planes
Part 5: Flock geometries
Chapter 7: Related geometries
1. Kantor’s coset technique
2. Quasi-BLT-sets
3. s-Inversion & s-square
4. A census
5. Quasi-flock derivations
6. Herds of hyperovals
7. Hyperbolic fibrations
8. The correspondence theorem
9. Flocks to cyclic planes
Part 6: Twisted hyperbolic flocks
Chapter 8: Hyperbolic flocks and generalizations
1. Algebraic theory of twisted hyperbolic flocks
2. Simultaneous α-flocks & twisted hyperbolic spreads
3. Flocks of D-cones
4. j−planes and twisted hyperbolic flocks
5. Joint theory of α-flocks
6. The Kα-Klein quadric
7. Baer theory
8. Quasi-flocks
9. The Baer forms
10. Algebraic and α-Klein methods
11. Infinite flocks of hyperbolic quadrics
Part 7: Lifting
Chapter 9: Chains & surjectivity of degree 1/k
1. Restricted surjectivity
2. Hughes-Kleinfield look-alikes
3. The remaining quasifibrations of dimension 2
4. Large dimension quasifibrations
5. T-copies of generalized twisted field planes
Part 8: Lifting skewfields
Chapter 10: General theory
1. Matrix forms and replacement
2. The general skewfield spread
3. Generalized quaternion division rings
4. Retraction
Part 9: Bilinearity
Chapter 11: General bilinear geometries
1. Star flocks and rigidity
2. Bilinear α-flocks
3. Bilinear flocks of quadratic cones
4. Translation planes admitting SL(2,K)
5. Double covers
6. nm-Linear flocks of quadratic cones
7. Nests of reguli
8. Group replaceable translation planes
9. Circle geometry over K(√γ)
10.
-nest planes
11. Flocks of elliptic quadrics
12. Klein quadric and Pappian spreads
13. n-Linear elliptic flocks
14. Tangential packings of ovoids
Part 10: Multiple replacement theorem
Chapter 12: The general theorem
1. Skewfields of finite dimension/Fixσ
2. (a, b)K–inner automorphisms.
3. Automorphisms of infinite order
4. (a, b)K(θ)K⊗K K(ρ)-outer automorphisms
5. Cyclic algebras and additive quasifibrations
6. Cyclic division ring automorphisms
Part 11: Classification of subplane covered nets
Chapter 13: Suspect subplane covered nets
1. Ambient theory for subplane covered nets
2. Fundamentals of Kummer theory
3. Galois theory for division rings
4. Galois division rings & applications of multiple replacement
5. p-Adic numbers and Hensel’s lemma
6. Field extensions of Qp
7. The quaternion division rings (a, b)Qp
Part 12: Extensions of skewfields
Chapter 14: Quaternion division ring extensions
1. Ore’s method of localization of a ring
2. Skew polynomial rings
3. Generalized cyclic algebras
4. Extending division rings using rational function fields
5. Derivable nets over twisted formal Laurent series
6. Lifted semifields in PG(3,L(ρ))
7. A garden of division rings & multiple replacements
Chapter 15: General ideas on Klein extensions
1. Klein varieties
2. Translation planes admitting twisted pseudo-regulus nets
3. Skewfield α-flocks
4. Skewfield ‘cyclic’ translation planes
5. Spreads of large dimension
6. Finite and infinite theories of flocks
7. Division ring connections
8. Group theoretic differences
9. Specific differences in the theory
10. Hyperbolic flocks, finite and infinite
11. Remarks on corrections to earlier work
Bibliography
Index 
