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Book Summary
About the Book: Introduction to Homotopy Theory
Homotopy theory, which is the main part of algebraic topology, studies
topological objects up to homotopy equivalence. Homotopy equivalence is weaker
relations than topological equivalence, i.e., homotopy classes of spaces are
larger than homeomorphism classes. Even though the ultimate goal of topology is
to classify various classes of topological spaces up to a homeomorphism, in
algebraic topology, homotopy equivalence plays a more important role than
homeomorphism, essentially because the basic tools of algebraic topology
(homology and homotopy groups) are invariant with respect to homotopy
equivalence, and do not distinguish topologically nonequivalent, but homotopic
objects. The idea of homotopy can be turned into
- ISBN-13
- 9781681171852
- Language
- English
- Binding
- Hard Bound
- Publisher
- Scitus Academics LLC
- Publishing Date
- 2016
- Total Pages
- 280
Introduction to Homotopy Theory
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Product Specifications
Book Summary
About the Book: Introduction to Homotopy Theory
Homotopy theory, which is the main part of algebraic topology, studies
topological objects up to homotopy equivalence. Homotopy equivalence is weaker
relations than topological equivalence, i.e., homotopy classes of spaces are
larger than homeomorphism classes. Even though the ultimate goal of topology is
to classify various classes of topological spaces up to a homeomorphism, in
algebraic topology, homotopy equivalence plays a more important role than
homeomorphism, essentially because the basic tools of algebraic topology
(homology and homotopy groups) are invariant with respect to homotopy
equivalence, and do not distinguish topologically nonequivalent, but homotopic
objects. The idea of homotopy can be turned into
Book Specifications
- ISBN-13
- 9781681171852
- Language
- English
- Binding
- Hard Bound
- Publisher
- Scitus Academics LLC
- Publishing Date
- 2016
- Total Pages
- 280