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Floer homology groups in Yang-Mills theory /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Floer homology groups in Yang-Mills theory // S.K. Donaldson with the assistance of M. Furuta and D. Kotschick.
作者:	Donaldson, S. K.,
其他作者:	Furuta, M.,
面頁冊數:	1 online resource (vii, 236 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Yang-Mills theory. -
電子資源:	https://doi.org/10.1017/CBO9780511543098
ISBN:	9780511543098 (ebook)

Floer homology groups in Yang-Mills theory /
Donaldson, S. K.,

Floer homology groups in Yang-Mills theory /S.K. Donaldson with the assistance of M. Furuta and D. Kotschick. - 1 online resource (vii, 236 pages) :digital, PDF file(s). - Cambridge tracts in mathematics ;147. - Cambridge tracts in mathematics ;203..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Yang-Mills theory over compact manifolds --

The concept of Floer homology was one of the most striking developments in differential geometry. It yields rigorously defined invariants which can be viewed as homology groups of infinite-dimensional cycles. The ideas led to great advances in the areas of low-dimensional topology and symplectic geometry and are intimately related to developments in Quantum Field Theory. The first half of this book gives a thorough account of Floer's construction in the context of gauge theory over 3 and 4-dimensional manifolds. The second half works out some further technical developments of the theory, and the final chapter outlines some research developments for the future - including a discussion of the appearance of modular forms in the theory. The scope of the material in this book means that it will appeal to graduate students as well as those on the frontiers of the subject.

ISBN: 9780511543098 (ebook)Subjects--Topical Terms:

857745
Yang-Mills theory.

LC Class. No.: QC174.52.Y37 / D66 2002

Dewey Class. No.: 530.14/35

Floer homology groups in Yang-Mills theory /
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 0 $t Yang-Mills theory over compact manifolds -- $t The case of a compact 4-manifold -- $t Technical results -- $t Manifolds with tubular ends -- $t Yang-Mills theory and 3-manifolds -- $t Initial discussion -- $t The Chern-Simons functional -- $t The instanton equation -- $t Linear operators -- $t Appendix A: local models -- $t Appendix B: pseudo-holomorphic maps -- $t Appendix C: relations with mechanics -- $t Linear analysis -- $t Separation of variables -- $t Sobolev spaces on tubes -- $t Remarks on other operators -- $t The addition property -- $t Weighted spaces -- $t Floer's grading function; relation with the Atiyah, Patodi, Singer theory -- $t Refinement of weighted theory -- $t L[superscript p] theory -- $t Gauge theory and tubular ends -- $t Exponential decay -- $t Moduli theory -- $t Moduli theory and weighted spaces -- $t Gluing instantons -- $t Gluing in the reducible case -- $t Appendix A: further analytical results -- $t Convergence in the general case -- $t Gluing in the Morse--Bott case -- $t The Floer homology groups -- $t Compactness properties -- $t Floer's instanton homology groups -- $t Independence of metric -- $t Orientations -- $t Deforming the equations -- $t Transversality arguments -- $t U(2) and SO(3) connections -- $t Floer homology and 4-manifold invariants -- $t The conceptual picture -- $t The straightforward case -- $t Review of invariants for closed 4-manifolds -- $t Invariants for manifolds with boundary and b[superscript +]] 1 -- $t Reducible connections and cup products -- $t The maps D[subscript 1], D[subscript 2] -- $t Manifolds with b[superscript +] = 0, 1 -- $t The case b[superscript +] = 1.
520 $a The concept of Floer homology was one of the most striking developments in differential geometry. It yields rigorously defined invariants which can be viewed as homology groups of infinite-dimensional cycles. The ideas led to great advances in the areas of low-dimensional topology and symplectic geometry and are intimately related to developments in Quantum Field Theory. The first half of this book gives a thorough account of Floer's construction in the context of gauge theory over 3 and 4-dimensional manifolds. The second half works out some further technical developments of the theory, and the final chapter outlines some research developments for the future - including a discussion of the appearance of modular forms in the theory. The scope of the material in this book means that it will appeal to graduate students as well as those on the frontiers of the subject.
650 0 $a Yang-Mills theory. $3 857745
650 0 $a Floer homology. $3 1022466
650 0 $a Geometry, Differential. $3 527830
700 1 $a Furuta, M., $e author. $3 1444465
700 1 $a Kotschick, D., $e author. $3 1444466
776 0 8 $i Print version: $z 9780521808033
830 0 $a Cambridge tracts in mathematics ; $v 203. $3 1238301
856 4 0 $u https://doi.org/10.1017/CBO9780511543098