By Victor Guillemin
This article suits any direction with the notice "Manifold" within the identify. it's a graduate point ebook.
By Kevin Lin, Zhenghan Wang, Weiping Zhang
This targeted quantity, due to a convention on the Chern Institute of arithmetic devoted to the reminiscence of Xiao-Song Lin, offers a wide connection among topology and physics as exemplified via the connection among low-dimensional topology and quantum box thought. the amount contains works on photograph (2+1) - TQFTs and their purposes to quantum computing, categorification and Khovanov homology, Gromov - Witten variety invariants, twisted Alexander polynomials, Faddeev knots, generalized Ricci move, Calabi - Yau difficulties for CR manifolds, Milnor's conjecture on quantity of simplexes, Heegaard genera of 3-manifolds, and the (A,B) - slice challenge. additionally it is 5 unpublished papers of Xiao-Song Lin and diverse speeches regarding the memorial convention.
By Philippe Gille
This ebook is the 1st complete, smooth creation to the idea of significant easy algebras over arbitrary fields. ranging from the fundamentals, it reaches such complex effects because the Merkurjev-Suslin theorem. This theorem is either the fruits of labor initiated by means of Brauer, Noether, Hasse and Albert and the start line of present learn in motivic cohomology idea by way of Voevodsky, Suslin, Rost and others. Assuming just a sturdy historical past in algebra, yet no homological algebra, the ebook covers the fundamental conception of significant uncomplicated algebras, tools of Galois descent and Galois cohomology, Severi-Brauer kinds, residue maps and, ultimately, Milnor K-theory and K-cohomology. The final bankruptcy rounds off the speculation via proposing the implications in optimistic attribute, together with the concept of Bloch-Gabber-Kato. The ebook is acceptable as a textbook for graduate scholars and as a reference for researchers operating in algebra, algebraic geometry or K-theory.
By Michael Farber
This monograph is an creation to the interesting box of the topology, geometry and dynamics of closed one-forms. the topic was once initiated through S. P. Novikov in 1981 as a examine of Morse style zeros of closed one-forms. the 1st chapters of the booklet, written in textbook sort, provide a close exposition of Novikov idea, which performs a basic position in geometry and topology. next chapters of the e-book current quite a few themes the place closed one-forms play a crucial function. the main major effects are the subsequent: the answer of the matter of exactness of the Novikov inequalities for manifolds with the countless cyclic primary staff. the answer of an issue raised via E. Calabi approximately intrinsically harmonic closed one-forms and their Morse numbers. the development of a common chain advanced which bridges the topology of the underlying manifold with information regarding zeros of closed one-forms. This complicated implies many fascinating inequalities together with Bott-type inequalities, equivariant inequalities, and inequalities concerning von Neumann Betti numbers. the development of a unique Lusternik-Schnirelman-type idea for dynamical platforms. Closed one-forms seem in dynamics in the course of the proposal of a Lyapunov one-form of a movement. As is proven within the publication, homotopy conception can be used to foretell the life of homoclinic orbits and homoclinic cycles in dynamical platforms (""focusing effect"")
By Peter A Firby, Cyril F Gardiner
This up-to-date and revised variation of a greatly acclaimed and profitable textual content for undergraduates examines topology of contemporary compact surfaces during the improvement of easy principles in airplane geometry. Containing over 171 diagrams, the method makes it possible for an easy therapy of its topic quarter. it really is really appealing for its wealth of purposes and diversity of interactions with branches of arithmetic, associated with floor topology, graph concept, crew concept, vector box thought, and airplane Euclidean and non-Euclidean geometry.
By Ralph L. Cohen
This publication explores string topology, Hochschild and cyclic homology, assembling fabric from a large scattering of scholarly resources in one functional quantity. the 1st half bargains an intensive and stylish exposition of varied techniques to thread topology and the Chas-Sullivan loop product. the second one offers an entire and transparent development of an algebraic version for computing topological cyclic homology.