The ebook explores the opportunity of extending the notions of "Grassmannian" and "Gauss map" to the PL classification. they're uncommon from "classifying house" and "classifying map" that are basically homotopy-theoretic notions. The analogs of Grassmannian and Gauss map outlined include geometric and combinatorial details. important functions contain attribute classification conception, smoothing conception, and the life of immersion satifying convinced geometric standards, e.g. curvature stipulations. The publication assumes wisdom of easy differential topology and package idea, together with Hirsch-Gromov-Phillips thought, in addition to the analogous theories for the PL class. The paintings may be of curiosity to mathematicians focused on geometric topology, PL and PD elements of differential geometry and the geometry of polyhedra.
By Lefschetz S.
By Dmitry Kozlov
This quantity is the 1st complete therapy of combinatorial algebraic topology in ebook shape. the 1st a part of the publication constitutes a speedy stroll during the major instruments of algebraic topology. Readers - graduate scholars and dealing mathematicians alike - will most likely locate quite priceless the second one half, which includes an in-depth dialogue of the most important learn suggestions of combinatorial algebraic topology. even supposing purposes are sprinkled during the moment half, they're important concentration of the 3rd half, that's completely dedicated to constructing the topological constitution conception for graph homomorphisms.
By G.M. Khenkin, Jaak Peetre, I.M. Dektyarev, O.M. Khudaverdyan, V.Ya. Lin, S.I. Pinchuk, E.A. Poletskii, L.I. Ronkin, A.A. Roslyi,
We contemplate the fundamental difficulties, notions and evidence within the conception of complete features of numerous variables, i. e. capabilities J(z) holomorphic within the complete n house 1 the 0 set of a whole functionality isn't discrete and accordingly one has no analogue of a device akin to the canonical Weierstrass product, that's basic within the case n = 1. moment, for n> 1 there exist a number of assorted average methods of laborious the distance
By Kasner E.
By Arthur Ogus
By Edited by R. H. Fox, D. C. Spencer, A. W. Tucker
By Junming Xu
This e-book presents the main simple difficulties, recommendations, and well-established effects from the topological constitution and research of interconnection networks within the graph-theoretic language. It covers the fundamental rules and techniques of community layout, numerous recognized networks similar to hypercubes, de Bruijn digraphs, Kautz digraphs, double loop, and different networks, and the most recent parameters to degree functionality of fault-tolerant networks similar to Menger quantity, Rabin quantity, fault-tolerant diameter, wide-diameter, limited connectivity, and (l,w)-dominating quantity. viewers: The e-book is appropriate for these readers who're operating on or intend to begin study in layout research of the topological constitution of interconnection networks, fairly undergraduates and postgraduates focusing on laptop technology and utilized arithmetic.
By Anderson D.R., Munkholm H.J.
By Eduard Casas-Alvero, Gerald E. Welters, Sebastian Xambo-Descamps