By Yong-Geun Oh
By Yuli Rudyak
The examine of triangulations of topological areas has consistently been on the root of geometric topology. one of the such a lot studied triangulations are piecewise linear triangulations of high-dimensional topological manifolds. Their learn culminated within the overdue 1960s–early Nineteen Seventies in a whole type within the paintings of Kirby and Siebenmann. it really is this class that we talk about during this publication, together with the prestigious Hauptvermutung and Triangulation Conjecture.
The objective of this ebook is to supply a readable and well-organized exposition of the topic, which might be compatible for complicated graduate scholars in topology. An exposition like this can be at the moment lacking.
By Claire Voisin
In this ebook, Claire Voisin offers an advent to algebraic cycles on complicated algebraic types, to the key conjectures concerning them to cohomology, or even extra accurately to Hodge buildings on cohomology. the amount is meant for either scholars and researchers, and never purely offers a survey of the geometric equipment constructed within the final thirty years to appreciate the well-known Bloch-Beilinson conjectures, but additionally examines fresh paintings via Voisin. The e-book specializes in vital gadgets: the diagonal of a variety—and the partial Bloch-Srinivas style decompositions it will possibly have looking on the dimensions of Chow groups—as good as its small diagonal, that's the proper item to think about that allows you to comprehend the hoop constitution on Chow teams and cohomology. An exploration of a sampling of contemporary works by way of Voisin appears to be like on the relation, conjectured normally by means of Bloch and Beilinson, among the coniveau of normal entire intersections and their Chow teams and a truly specific estate happy by way of the Chow ring of K3 surfaces and conjecturally by means of hyper-Kähler manifolds. particularly, the e-book delves into arguments originating in Nori's paintings which have been additional constructed by way of others.
By J. Śniatycki
By Sigurdur Helgason
By János Pach
In many purposes of graph concept, graphs are considered as geometric gadgets drawn within the aircraft or in another floor. the normal tools of "abstract" graph conception are frequently incapable of delivering passable solutions to questions coming up in such functions. long ago couple of a long time, many robust new combinatorial and topological suggestions were built to take on those difficulties. this present day geometric graph concept is a burgeoning box with many remarkable effects and attractive open questions.
This contributed quantity comprises thirty unique survey and study papers on vital fresh advancements in geometric graph theory. The contributions have been completely reviewed and written by means of very good researchers during this field.
By Anant R. Shastri
Derived from the author’s path at the topic, Elements of Differential Topology explores the colossal and chic theories in topology built by means of Morse, Thom, Smale, Whitney, Milnor, and others. It starts with differential and quintessential calculus, leads you thru the intricacies of manifold concept, and concludes with discussions on algebraic topology, algebraic/differential geometry, and Lie groups.
The first chapters assessment differential and fundamental calculus of a number of variables and current basic effects which are used in the course of the textual content. the following couple of chapters concentrate on delicate manifolds as submanifolds in a Euclidean house, the algebraic equipment of differential types helpful for learning integration on manifolds, summary tender manifolds, and the root for homotopical elements of manifolds. the writer then discusses a imperative topic of the e-book: intersection thought. He additionally covers Morse capabilities and the fundamentals of Lie teams, which supply a wealthy resource of examples of manifolds. routines are integrated in each one bankruptcy, with strategies and tricks behind the book.
A sound advent to the idea of soft manifolds, this article guarantees a tender transition from calculus-level mathematical adulthood to the extent required to appreciate summary manifolds and topology. It includes all regular effects, reminiscent of Whitney embedding theorems and the Borsuk–Ulam theorem, in addition to numerous similar definitions of the Euler characteristic.
By Tamal K. Dey
By Károly Bezdek
This monograph offers a quick creation to the correct smooth elements of discrete geometry, as well as top the reader to the frontiers of geometric study on sphere preparations. The readership is geared toward complex undergraduate and early graduate scholars, in addition to researchers. It includes greater than forty open study difficulties excellent for graduate scholars and researchers in arithmetic and computing device technology. also, this e-book might be thought of perfect for a one-semester complicated undergraduate or graduate point path.
The middle a part of this e-book relies on 3 lectures given by way of the writer on the Fields Institute through the thematic software on “Discrete Geometry and functions” and comprises 4 middle subject matters. the 1st issues encompass lively parts which have been amazing from the start of discrete geometry, particularly dense sphere packings and tilings. Sphere packings and tilings have a truly powerful connection to quantity concept, coding, teams, and mathematical programming. Extending the culture of learning packings of spheres, is the research of the monotonicity of quantity less than contractions of arbitrary preparations of spheres. The 3rd significant subject of this booklet are available lower than the sections on ball-polyhedra that examine the potential for extending the speculation of convex polytopes to the relatives of intersections of congruent balls. This component to the textual content is hooked up in lots of how you can the above-mentioned significant issues and it's also attached to a couple different very important learn components because the one on coverings by means of planks (with shut ties to geometric analysis). This fourth center subject is mentioned below masking balls via cylinders.
By Edward R. Fadell,Sufian Y. Husseini
With purposes in brain, this self-contained monograph presents a coherent and thorough therapy of the configuration areas of Euclidean areas and spheres, making the topic obtainable to researchers and graduates with a minimum historical past in classical homotopy concept and algebraic topology.