Hoffman index of manifolds

Dissertant

Sadiq, Afra Radi

Thesis advisor

Fathi, Sakin A.

Comitee Members

Majid, Wasan Khalid
Majid, Abd al-Rahman Hamid
Khidr, Jihad Ramadan
al-Bahrani, Bahar Hamad Ahmad
Mansur, Nadir Jurj

University

University of Baghdad

Faculty

College of Science

Department

Mathematics Department

University Country

Iraq

Degree

Ph.D.

Degree Date

2007

English Abstract

Let X be a topological space and f : X ! X be a map, a point x 2 X is called a fixed point for f if f(x) = x and x is a periodic point if there exists k 2 N such that fk(x) = x.

More generally, if f, g : X ! X are maps, then a point x 2 X is a coincidence point for f and g if f(x) = g(x).

The no coincidence index is a topological invariant reflecting the number of fixed-point-free-self maps of a connected topological manifold M such that no pair of these maps has a coincidence.

This concept was introduced and studied by M.

Hoffman in 1984, he gave sufficient conditions for a manifold M, to have no coincidence index #M = 1.

Also he computed the no coincidence index for some important homogenous spaces (the flag manifolds).

In 1989 M.

Hoffman continued his study of this concept and he gave necessary and sufficient conditions for a manifold to have finite no coincidence index.

In this thesis, we study this concept and prove some results that are stated in the literature without proofs.

We also give details of the proofs of many important results, and illustrate these results by some examples.

We give some new results related to this concept.

We define two new indices, the homeomorphism no coincidence index and the period no coincidence index, and give some useful results for computing each of these indices.

Also we give results relating these indices with the no coincidence index of Hoffman.

Main Subjects

Mathematics

Topics

• Mathematical models

No. of Pages

134

Table of Contents

• APA
• MLA
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Language

English

Data Type

Arab Theses

Record ID

BIM-603137