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  3. Floer Homology Groups in Yang-Mills Theory
  • Cited by 109
Publisher:
Cambridge University Press
Online publication date:
August 2009
Print publication year:
2002
Online ISBN:
9780511543098
DOI:
https://doi.org/10.1017/CBO9780511543098
Subjects:
Mathematics (general), Mathematics, Mathematical Physics, Geometry and Topology
Series:
Cambridge Tracts in Mathematics (147)
Information

Book description

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.

Reviews

‘… relatively short but very infomative, modern and clearly written … I stronly recommend the book to both specialists and graduate students’.

S. Merkulov Source: Proceedings of the Edinburgh Mathematical Society

‘… a compact but very readable account.’

Source: Mathematika

'… gives a nice account of the theory of an interesting topic in contemporary geometry and topology. It can be strongly recommended …'.

Source: EMS Newsletter

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