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Floer homology groups in Yang-Mills theory

Author: S K Donaldson; M Furuta; D Kotschick
Publisher: Cambridge ; New York : Cambridge University Press, 2002.
Series: Cambridge tracts in mathematics, 147.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Fields-medal winner Donaldson reviews current work, including his own, on the theory of Floer.

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: S K Donaldson; M Furuta; D Kotschick
ISBN: 0521808030 9780521808033
OCLC Number: 47056362
Description: vii, 236 pages ; 24 cm.
Contents: Yang-Mills theory over compact manifolds --
The case of a compact 4-manifold --
Technical results --
Manifolds with tubular ends --
Yang-Mills theory and 3-manifolds --
Initial discussion --
The Chern-Simons functional --
The instanton equation --
Linear operators --
Appendix A: local models --
Appendix B: pseudo-holomorphic maps --
Appendix C: relations with mechanics --
Linear analysis --
Separation of variables --
Sobolev spaces on tubes --
Remarks on other operators --
The addition property --
Weighted spaces --
Floer's grading function; relation with the Atiyah, Patodi, Singer theory --
Refinement of weighted theory --
L[superscript p] theory --
Gauge theory and tubular ends --
Exponential decay --
Moduli theory --
Moduli theory and weighted spaces --
Gluing instantons --
Gluing in the reducible case --
Appendix A: further analytical results --
Convergence in the general case --
Gluing in the Morse--Bott case --
The Floer homology groups --
Compactness properties --
Floer's instanton homology groups --
Independence of metric --
Orientations --
Deforming the equations --
Transversality arguments --
U(2) and SO(3) connections --
Floer homology and 4-manifold invariants --
The conceptual picture --
The straightforward case --
Review of invariants for closed 4-manifolds --
Invariants for manifolds with boundary and b[superscript +]] 1 --
Reducible connections and cup products --
The maps D[subscript 1], D[subscript 2] --
Manifolds with b[superscript +] = 0, 1 --
The case b[superscript +] = 1.
Series Title: Cambridge tracts in mathematics, 147.
Responsibility: S.K. Donaldson with the assistance of M. Furuta and D. Kotschick.
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'... relatively short but very infomative, modern and clearly written ... I stronly recommend the book to both specialists and graduate students'. S. Merkulov, Proceedings of the Edinburgh Read more...

 
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