By Wolfgang Lück
In algebraic topology a few classical invariants - equivalent to Betti numbers and Reidemeister torsion - are outlined for compact areas and finite staff activities. they are often generalized utilizing von Neumann algebras and their strains, and utilized additionally to non-compact areas and countless teams. those new L2-invariants comprise very fascinating and novel details and will be utilized to difficulties bobbing up in topology, K-Theory, differential geometry, non-commutative geometry and spectral conception. it truly is fairly those interactions with diversified fields, that make L2-invariants very robust and interesting. The booklet provides a accomplished advent to this region of analysis, in addition to its latest effects and advancements. it's written in a fashion which allows the reader to pick his favorite subject and to discover the outcome he or she is attracted to quick and with no being compelled to head via different fabric.
By Thomas F. Banchoff, Stephen T. Lovett
Preface Acknowledgements aircraft Curves: neighborhood houses Parameterizations place, speed, and Acceleration Curvature Osculating Circles, Evolutes, and Involutes usual Equations airplane Curves: international homes uncomplicated homes Rotation Index Isoperimetric Inequality Curvature, Convexity, and the Four-Vertex Theorem Curves in house: neighborhood homes Definitions, Examples, and Differentiation Curvature, Torsion, and the Frenet body Osculating aircraft and Osculating Sphere typical Equations Curves in house: international houses uncomplicated homes Indicatrices and overall Curvature Knots and hyperlinks Re. Read more...
summary: Preface Acknowledgements aircraft Curves: neighborhood houses Parameterizations place, pace, and Acceleration Curvature Osculating Circles, Evolutes, and Involutes average Equations airplane Curves: worldwide houses uncomplicated homes Rotation Index Isoperimetric Inequality Curvature, Convexity, and the Four-Vertex Theorem Curves in area: neighborhood houses Definitions, Examples, and Differentiation Curvature, Torsion, and the Frenet body Osculating airplane and Osculating Sphere average Equations Curves in area: international houses simple houses Indicatrices and overall Curvature Knots and hyperlinks Re
By Luther Pfahler Eisenhart
The various earliest books, quite these courting again to the 1900s and sooner than, at the moment are super scarce and more and more dear. we're republishing those vintage works in cheap, prime quality, smooth variations, utilizing the unique textual content and art.
By Ana Cannas da Silva
The aim of those notes is to supply a quick advent to symplectic geometry for graduate scholars with a few wisdom of differential geometry, de Rham conception and classical Lie groups.
This textual content addresses symplectomorphisms, neighborhood types, touch manifolds, suitable nearly advanced constructions, Kaehler manifolds, hamiltonian mechanics, second maps, symplectic relief and symplectic toric manifolds. It comprises guided difficulties, referred to as homework, designed to counterpoint the exposition or expand the reader's understanding.
There are by means of now first-class references on symplectic geometry, a subset of that's within the bibliography of this publication. although, the most productive advent to an issue is usually a brief ordinary remedy, and those notes try and serve that objective. this article offers a style of parts of present examine and should arrange the reader to discover fresh papers and huge books on symplectic geometry the place the velocity is far faster.
For this reprint various corrections and clarifications were made, and the format has been improved.
By Giampiero Esposito
The Dirac operator has many helpful functions in theoretical physics and arithmetic. This e-book offers a transparent, concise and self-contained advent to the worldwide conception of the Dirac operator and to the research of spectral asymptotics with neighborhood or nonlocal boundary stipulations. the idea is brought at a degree appropriate for graduate scholars. a variety of examples are then given to demonstrate the unusual houses of the Dirac operator, and the function of boundary stipulations in heat-kernel asymptotics and quantum box thought. subject matters coated comprise the advent of spin-structures in Riemannian and Lorentzian manifolds; functions of index concept; heat-kernel asymptotics for operators of Laplace kind; quark boundary stipulations; one-loop quantum cosmology; conformally covariant operators; and the position of the Dirac operator in a few contemporary investigations of four-manifolds. This quantity presents graduate scholars with a rigorous advent and researchers with a valuable connection with the Dirac operator and its functions in theoretical physics.
By Shigeyuki Morita
This books offers a really direct clarification of the most ideas in differential types. i'd suggest it for somebody eager to get to the most innovations quick and cleanly.
By Jürgen Jost
Even if Riemann surfaces are a time-honoured box, this booklet is novel in its extensive standpoint that systematically explores the relationship with different fields of arithmetic. it will possibly function an creation to modern arithmetic as an entire because it develops historical past fabric from algebraic topology, differential geometry, the calculus of adaptations, elliptic PDE, and algebraic geometry. it really is particular between textbooks on Riemann surfaces in together with an creation to Teichm?ller conception. The analytic process is also new because it relies at the idea of harmonic maps.