Casson's Invariant for Oriented Homology Three-Spheres (eBook)

An Exposition

Selman Akbulut, John D. McCarthy (Autoren)

eBook Download: PDF

2014
Princeton University Press (Verlag)
978-1-4008-6062-3 (ISBN)

Infos

In the spring of 1985, A. Casson announced an interesting invariant of homology 3-spheres via constructions on representation spaces. This invariant generalizes the Rohlin invariant and gives surprising corollaries in low-dimensional topology. In the fall of that same year, Selman Akbulut and John McCarthy held a seminar on this invariant. These notes grew out of that seminar. The authors have tried to remain close to Casson's original outline and proceed by giving needed details, including an exposition of Newstead's results. They have often chosen classical concrete approaches over general methods. For example, they did not attempt to give gauge theory explanations for the results of Newstead; instead they followed his original techniques.Originally published in 1990.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Produkt-Details

• Erscheint lt. Verlag: 14.7.2014
• Reihe/Serie: Mathematical Notes
• Reihe/Serie: Mathematical Notes
• Reihe/Serie: Princeton Legacy Library
• Reihe/Serie: Princeton Legacy Library
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Technik
• Schlagworte: 3-manifold • 3-sphere • Addition • Alexander polynomial • Algebraic Structure • Ambient isotopy • Arf invariant • automorphism • Career • Charles Darwin • coefficient • cohomology • Commutative diagram • conjugacy class • corollary • cotangent space • Darwinism • Dehn surgery • Dehn twist • Diagonal matrix • Diagram (category theory) • diffeomorphism • differentiable manifold • E8 manifold • existential quantification • Explanation • Exponential map (Lie theory) • Exponential map (Riemannian geometry) • fiber bundle • fibration • Gauge Theory • Heegaard splitting • Homeomorphism • Homology (mathematics) • homology sphere • Homomorphism • Homotopy • Integer • Intersection form (4-manifold) • Intersection number (graph theory) • irreducible representation • Knot invariant • Lie algebra • Lie group • Linear combination • Linear map • longitude • Low-dimensional topology • manifold • Mathematical Induction • Mode of action • Natural number • Neighbourhood (mathematics) • Nomenclature • Normal (geometry) • Notation • Parity (mathematics) • Pointwise • polynomial • Public Opinion • pullback • quaternion • Quotient space (linear algebra) • Radicalism (historical) • result • Rewriting • Second derivative • Seifert Surface • simplicial complex • Smooth structure • Social Movement • Sociocultural evolution • Sphere • submanifold • Subset • Summation • Support (mathematics) • syndicalism • Theorem • Topological Manifold • torus • transcendental number • Triviality (mathematics) • Typing • un-american • uniqueness • unknot • Unlink • Vector Space • Writing
• ISBN-10: 1-4008-6062-8 / 1400860628
• ISBN-13: 978-1-4008-6062-3 / 9781400860623