Basic Concepts Of Algebraic Topology (undergraduate Texts In Mathematics)
by Fred H. Croom /
1978 / English / PDF
3.9 MB Download
This text is intended as a one semester introduction to algebraic
topology at the undergraduate and beginning graduate levels.
Basically, it covers simplicial homology theory, the fundamental
group, covering spaces, the higher homotopy groups and introductory
singular homology theory. The text follows a broad historical
outline and uses the proofs of the discoverers of the important
theorems when this is consistent with the elementary level of the
course. This method of presentation is intended to reduce the
abstract nature of algebraic topology to a level that is palatable
for the beginning student and to provide motivation and cohesion
that are often lacking in abstact treatments. The text emphasizes
the geometric approach to algebraic topology and attempts to show
the importance of topological concepts by applying them to problems
of geometry and analysis. The prerequisites for this course are
calculus at the sophomore level, a one semester introduction to the
theory of groups, a one semester introduc- tion to point-set
topology and some familiarity with vector spaces. Outlines of the
prerequisite material can be found in the appendices at the end of
the text. It is suggested that the reader not spend time initially
working on the appendices, but rather that he read from the
beginning of the text, referring to the appendices as his memory
needs refreshing. The text is designed for use by college juniors
of normal intelligence and does not require "mathematical maturity"
beyond the junior level.
This text is intended as a one semester introduction to algebraic
topology at the undergraduate and beginning graduate levels.
Basically, it covers simplicial homology theory, the fundamental
group, covering spaces, the higher homotopy groups and introductory
singular homology theory. The text follows a broad historical
outline and uses the proofs of the discoverers of the important
theorems when this is consistent with the elementary level of the
course. This method of presentation is intended to reduce the
abstract nature of algebraic topology to a level that is palatable
for the beginning student and to provide motivation and cohesion
that are often lacking in abstact treatments. The text emphasizes
the geometric approach to algebraic topology and attempts to show
the importance of topological concepts by applying them to problems
of geometry and analysis. The prerequisites for this course are
calculus at the sophomore level, a one semester introduction to the
theory of groups, a one semester introduc- tion to point-set
topology and some familiarity with vector spaces. Outlines of the
prerequisite material can be found in the appendices at the end of
the text. It is suggested that the reader not spend time initially
working on the appendices, but rather that he read from the
beginning of the text, referring to the appendices as his memory
needs refreshing. The text is designed for use by college juniors
of normal intelligence and does not require "mathematical maturity"
beyond the junior level.
