Differential Forms and Cohomology: Course
by Peter Saveliev
Publisher: Intelligent Perception 2013
Differential forms provide a modern view of calculus. They also give you a start with algebraic topology in the sense that one can extract topological information about a manifold from its space of differential forms. It is called cohomology.
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The aim of this book is to describe significant topics in topological group theory in the early 21st century as well as providing some guidance to the future directions topological group theory might take by including some interesting open questions.
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This is a comprehensive introduction to the theory of stable commutator length, an important subfield of quantitative topology, with substantial connections to 2-manifolds, dynamics, geometric group theory, bounded cohomology, symplectic topology.
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