By Loring W. Tu
Manifolds, the higher-dimensional analogs of tender curves and surfaces, are primary gadgets in smooth arithmetic. Combining features of algebra, topology, and research, manifolds have additionally been utilized to classical mechanics, basic relativity, and quantum box theory.
In this streamlined advent to the topic, the idea of manifolds is gifted with the purpose of assisting the reader in achieving a speedy mastery of the fundamental subject matters. via the top of the ebook the reader will be in a position to compute, not less than for easy areas, the most easy topological invariants of a manifold, its de Rham cohomology. alongside the best way the reader acquires the data and talents worthwhile for extra examine of geometry and topology. The needful point-set topology is integrated in an appendix of twenty pages; different appendices evaluate evidence from actual research and linear algebra. tricks and strategies are supplied to a few of the routines and problems.
This paintings can be used because the textual content for a one-semester graduate or complicated undergraduate direction, in addition to via scholars engaged in self-study. Requiring simply minimum undergraduate prerequisites, An Introduction to Manifolds is additionally a superb starting place for Springer GTM eighty two, Differential types in Algebraic Topology.
By Mark Gross, Daniel Huybrechts, Dominic Joyce, Geir Ellingsrud, Loren Olson, Kristian Ranestad, Stein A. Stromme
From the reviews:
"Summer colleges in Nordfjordeid, Norway, were geared up on a regular basis due to the fact that 1996. themes fluctuate every year yet there are continuously 3 sequence of lectures by way of invited specialists with night routines. […] the subjects of all 3 contributions are interrelated and jointly they provide a pleasant creation right into a very attention-grabbing box of study at the border among arithmetic and physics. l want to strongly suggest the e-book to anyone attracted to the topic."
(jbu) ecu Mathematical Society publication, Sept. 2004, p. 44
"[...] This publication is a superb creation to present learn within the geometry of Calabi-Yau manifolds, hyper-Kähler manifolds, unheard of holonomy and replicate symmetry. [...] this is often a good and helpful e-book. different chapters commonly healthy jointly kind of good [...]. it is going to be well-liked by someone attempting to find out about Kähler manifolds with c1=0 and reflect symmetry."
Richard P. Thomas, Mathematical stories, Clippings from factor 2004c
"Summer colleges in Nordfjordeid, Norway, were geared up on a regular basis seeing that 1996. … the varsity held in June 2001 was once dedicated to contemporary interplay among differential and algebraic geometry. The ebook involves notes written by means of academics of the corresponding 3 sequence of lectures. … they offer a pleasant creation right into a very attention-grabbing box of study at the border among arithmetic and physics. i want to strongly suggest the booklet to anyone drawn to the topic." (EMS, September, 2004)
"This ebook is a superb creation to present study within the geometry of Calabi-Yau manifolds, hyper-Kähler manifolds, remarkable holonomy and reflect symmetry. … the alternative of themes is a smart one. … this can be an outstanding and invaluable ebook. … it is going to be well-liked by someone attempting to find out about Kähler manifolds with c1 = zero and reflect symmetry." (Richard P. Thomas, Mathematical experiences, 2004 c)
By José G Vargas
It is a booklet that the writer needs were to be had to him whilst he was once pupil. It displays his curiosity in figuring out (like specialist mathematicians) the main correct arithmetic for theoretical physics, yet within the kind of physicists. which means one isn't dealing with the research of a set of definitions, comments, theorems, corollaries, lemmas, and so forth. yet a story — similar to a narrative being instructed — that doesn't abate sophistication and deep effects.
It covers differential geometry a long way past what common relativists understand they should understand. And it introduces readers to different parts of arithmetic which are of curiosity to physicists and mathematicians, yet are principally missed. between those is Clifford Algebra and its makes use of along side differential kinds and relocating frames. It opens new examine vistas that extend the subject material.
In an appendix at the classical thought of curves and surfaces, the writer slashes not just the most proofs of the conventional procedure, which makes use of vector calculus, yet even current remedies that still use differential types for a similar purpose.
Readership: Physicists and mathematicians engaged on differential geometry
By Frank Morgan
This vintage textual content serves as a device for self-study; it's also used as a simple textual content for undergraduate classes in differential geometry. The author's skill to extract the basic components of the speculation in a lucid and concise type permits the coed easy accessibility to the cloth and allows the teacher so as to add emphasis and canopy targeted themes. the extreme wealth of examples in the workouts and the recent fabric, starting from isoperimetric difficulties to reviews on Einstein's unique paper on relativity concept, improve this re-creation.
By Steve Alpern
This publication offers a self-contained creation to average houses of quantity retaining homeomorphisms, examples of which come with transitivity, chaos and ergodicity. The authors make the 1st a part of the publication very concrete via targeting quantity keeping homeomorphisms of the unit n-dimensional dice. additionally they end up fastened aspect theorems (Conley-Zehnder-Franks). this can be performed in a few brief self-contained chapters that might be compatible for an undergraduate research seminar or a graduate lecture path. elements and 3 give some thought to compact manifolds and sigma compact manifolds respectively, describing the paintings of the 2 authors in extending the distinguished results of Oxtoby and Ulam that for quantity homeomorphisms of the unit dice, ergodicity is a standard estate.