What do you do to start reading dimension theory? Searching the book that you love to read first or find an interesting book that will make you want to read? Everybody has difference with their reason of reading a book. Actuary, reading habit must be from earlier. Many people may be love to read, but not a book. It's not fault. Someone will be bored to open the thick book with small words to read. In more, this is the real condition. So do happen probably with this dimension theory.

Aspects of topology: On dimension theory

This paper compiles basic components of the construction of random groups and of the proof of their properties announced in [G10]. Justification of each step, as well as the interrelation between them, is straightforward by available techniques specific to each step. On the other hand, there are several ingredients that cannot be truly appreciated without extending the present framework. We shall indicate along the way possible developments, postponing full exposition to forthcoming articles expanding the following points touched upon in the present paper.

Random walk in random groups

This chapter and the next are adapted from a lecture published in the Proceedings of the Third Physics Workshop, held at the Institute of Theoretical and Experimental Physics, Moscow, in 1975. They focus on the uses of homotopy theory in physics, and especially on the calculation of homotopy groups. The next chapter summarizes briefly the ways in which homotopy theory can be applied to quantum field theory.

Elements of Homotopy Theory

The description for this book, Compositional Methods in Homotopy Groups of Spheres. (AM-49), will be forthcoming.

Composition methods in homotopy groups of spheres

Oxford University Press in Africa, 1927â80

We establish some basic theorems in dimension theory and absolute extensor theory in the coarse category of metric spaces Some of the statements in this category can be translated in general topology language by applying the Higson corona functor The relation of problems and results of this `Asymptotic Topology' to Novikov and similar conjectures is discussed

Asymptotic topology

The asymptotic dimension theory was founded by Gromov in the early 90s In this paper we give a survey of its recent history where we emphasize two of its features: an analogy with the dimension theory of compact metric spaces and applications to the theory of discrete groups

Asymptotic Dimension

We prove a version of the countable union theorem for asymp- totic dimension and we apply it to groups acting on asymptotically nite dimensional metric spaces. As a consequence we obtain the following nite dimensionality theorems. A) An amalgamated product of asymptotically nite dimensional groups has nite asymptotic dimension: asdimAC B< 1 . B) Suppose that G 0 is an HNN extension of a group G with asdimG < 1. Then asdimG 0 <1. C) Suppose that is Davis' group constructed from a group with asdim <1. Then asdim <1. AMS Classication 20H15; 20E34, 20F69

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On asymptotic dimension of groups

We prove an asymptotic analog of the classical Hurewicz theorem on mappings that lower dimension. This theorem allows us to find sharp upper bound estimates for the asymptotic dimension of groups acting on finite dimensional metric spaces and allows us to prove a useful extension theorem for asymptotic dimension. As applications we find upper bound estimates for the asymptotic dimension of nilpotent and polycyclic groups in terms of their Hirsch length. We are also able to improve the known upper bounds on the asymptotic dimension of fundamental groups of complexes of groups, amalgamated free products and the hyperbolization of metric spaces possessing the Higson property.

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A Hurewicz-type theorem for asymptotic dimension and applications to geometric group theory

CONTENTS Introduction § 1. Definition of cohomological dimension § 2. Bokshtein's inequalities § 3. Cohomological manifolds over finite groups § 4. The CE-problem § 5. Borsuk's problem References

https://iopscience.iop.org/article/10.1070/RM1988v043n04ABEH001900/pdf

Alexander Dranishnikov

Papers

Asymptotic topology

Asymptotic Dimension

On asymptotic dimension of groups

A Hurewicz-type theorem for asymptotic dimension and applications to geometric group theory

Homological dimension theory