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Involutions on manifolds

Author: Santiago López de Medrano
Publisher: Berlin [u.a.] Springer 1971
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete, N.F., 59
Edition/Format:   Print book : EnglishView all editions and formats
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Document Type: Book
All Authors / Contributors: Santiago López de Medrano
ISBN: 0387050922 9780387050928 3540050922 9783540050926
OCLC Number: 832438389
Description: IX, 102 S graph. Darst
Contents: 0 Notation, Conventions, Preliminaries.- I The Browder-Livesay Invariants.- I.1 Involutions of Spheres.- I.1.1 Desuspensions and Characteristic Submanifolds.- I.1.2 Equivariant Surgery.- I.1.3 The Desuspension Theorem.- I.1.4 Concordance of Desuspensions.- I.2 Involutions of Simply Connected Manifolds.- I.2.1 Characteristic Submanifolds and h-regularity.- I.2.2 The Browder-Livesay Invariants.- II Realization of the Browder-Livesay Invariants.- II.1 The Realization Theorem.- II.2 Constructions with Involutions.- II.2.1 M?TM*.- II.2.2 (T, Mn) # N.- II.3 Proof of Theorem II.1-D.- II.4 Proof of Theorem II.1-A.- II.5 Homology 3-Spheres.- II.6 Manifolds with the Same Regular Homotopy Type as Line Bundles over Projective Spaces.- II.7 Invariant Codimension 2 Spheres.- III Relations with Non-simply-connected Surgery Obstructions.- III.1 Normal Invariants.- III.1.1 Normal Maps, Cobordisms and Invariants.- III.1.2 G/PL, G/0.- III.1.3 Homotopy Triangulations and Smoothings.- III.2 Non-simply-connected Surgery Obstructions.- III.2.1 The Groups Ln(?, ?).- III.2.2 The Obstruction Groups for ?=?2.- III.3 Relations with the Browder-Livesay Invariants.- III.3.1 ln: BLn(?) ? Ln?1(?2, ? ?).- III.3.2 Ambient vs. Abstract Surgery Obstructions.- III.3.3 Proof of Lemma 2, II.4.- III.3.4 Proof of Theorem II.1-C.- IV Combinatorial Classification of Involutions.- IV.1 Some Maps and Exact Sequences.- IV.2 Computation of [Pn, G/PL].- IV.3 The Classification Theorem.- IV.3.1 Homotopy Projective Spaces.- IV.3.2 Suspension.- IV.3.3 Two Useful Theorems.- IV.3.4 The Classification Theorem.- IV.3.5 Proof of Theorem II.1-B (p.l. case).- IV.4 Another Relation with Non-simply-connected Surgery Obstructions.- IV.4.1 ?= +- ?.- IV.4.2 On Theorem II.1-C.- IV.5 On the Topological Classification of Involutions.- V Smooth Involutions.- V.1 General Remarks on Smooth Involutions of Spheres.- V.2 Normal Invariants and Browder-Livesay Invariants.- V.2.1 Involutions of Spheres.- V.2.2 Involutions of Simply-connected Manifolds.- V.2.3 ?= +- ? again.- V.3 Differentiable Structure of Spheres and Other Double Coverings.- V.4 Proof of Theorem II.1-B, Smooth Case.- V.5 Involutions and the Generalized Kervaire Invariant.- V.5.1 The Generalized Kervaire Invariant.- V.5.2 Odd Multiples of an Involution.- V.6 Smooth Involutions of Spheres of Low Dimension.- V.6.1 Involutions of 7-Spheres.- V.6.2 Spheres that Admit Involutions.- V.7 Action of ?n(??) (After Browder).- V.8 How to Prove ? = ?.- VI Codimension 2 Invariant Spheres.- VI.1 Invariant vs. Characteristic Spheres.- VI.2 Applications.- VI.2.1 A Non-embedding Result.- VI.2.2 Some Brieskorn-Hirzebruch Involutions.- VI.3 Knotted and Unknotted Codimension 2 Invariant Spheres.- VI.4 Cobordism Classes of Invariant Knots.- Some Unsolved Problems.- References.- List of Symbols.
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete, N.F., 59
Responsibility: S. López de Medrano
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