By Liviu Nicolaescu
This is the 1st textbook to incorporate themes equivalent to Morse-Smale flows, min-max concept, second maps and equivariant cohomology, and complicated Morse idea. The exposition is better with examples, difficulties, and illustrations, and should be of curiosity to graduate scholars in addition to researchers. The reader is predicted to have a few familiarity with cohomology idea and with the differential and fundamental calculus on gentle manifolds.
Liviu Nicolaescu is affiliate Professor of arithmetic at collage of Notre Dame.
Read Online or Download An Invitation to Morse Theory (Universitext) PDF
Best geometry & topology books
Taking an instantaneous path, 'Essential Topology' brings an important facets of recent topology nearby of a second-year undergraduate pupil. It starts with a dialogue of continuity and, when it comes to many examples, results in the prestigious 'Hairy Ball theorem' and directly to homotopy and homology: the cornerstones of latest algebraic topology.
Algebraic K-theory encodes vital invariants for a number of mathematical disciplines, spanning from geometric topology and sensible research to quantity idea and algebraic geometry. As is often encountered, this strong mathematical item is particularly not easy to calculate. except Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few entire calculations have been to be had earlier than the invention of homological invariants provided via motivic cohomology and topological cyclic homology.
The learn of upper different types is attracting transforming into curiosity for its many purposes in topology, algebraic geometry, mathematical physics and class conception. during this hugely readable e-book, Carlos Simpson develops a whole set of homotopical algebra recommendations and proposes a operating thought of upper different types.
This quantity offers the development of canonical modular compactifications of moduli areas for polarized Abelian kinds (possibly with point structure), construction at the past paintings of Alexeev, Nakamura, and Namikawa.
- Twistor Theory (Lecture Notes in Pure and Applied Mathematics)
- Differential Characters (Lecture Notes in Mathematics)
- Introduction to Topology (De Gruyter Textbook)
- Riemannian Geometry (Graduate Texts in Mathematics)
- Complex Algebraic Curves (London Mathematical Society Student Texts)
Extra info for An Invitation to Morse Theory (Universitext)
An Invitation to Morse Theory (Universitext) by Liviu Nicolaescu