Algebraic Topology: An Intuitive Approach (translations Of Mathematical Monographs, Vol. 183)
by Hajime Sato /
1999 / English / PDF
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The single most difficult thing one faces when one begins to learn
a new branch of mathematics is to get a feel for the mathematical
sense of the subject. The purpose of this book is to help the
aspiring reader acquire this essential common sense about algebraic
topology in a short period of time. To this end, Sato leads the
reader through simple but meaningful examples in concrete terms.
Moreover, results are not discussed in their greatest possible
generality, but in terms of the simplest and most essential cases.
The single most difficult thing one faces when one begins to learn
a new branch of mathematics is to get a feel for the mathematical
sense of the subject. The purpose of this book is to help the
aspiring reader acquire this essential common sense about algebraic
topology in a short period of time. To this end, Sato leads the
reader through simple but meaningful examples in concrete terms.
Moreover, results are not discussed in their greatest possible
generality, but in terms of the simplest and most essential cases.
In response to suggestions from readers of the original edition
of this book, Sato has added an appendix of useful definitions
and results on sets, general topology, groups and such. He has
also provided references.
In response to suggestions from readers of the original edition
of this book, Sato has added an appendix of useful definitions
and results on sets, general topology, groups and such. He has
also provided references.
Topics covered include fundamental notions such as
homeomorphisms, homotopy equivalence, fundamental groups and
higher homotopy groups, homology and cohomology, fiber bundles,
spectral sequences and characteristic classes. Objects and
examples considered in the text include the torus, the Möbius
strip, the Klein bottle, closed surfaces, cell complexes and
vector bundles.
Topics covered include fundamental notions such as
homeomorphisms, homotopy equivalence, fundamental groups and
higher homotopy groups, homology and cohomology, fiber bundles,
spectral sequences and characteristic classes. Objects and
examples considered in the text include the torus, the Möbius
strip, the Klein bottle, closed surfaces, cell complexes and
vector bundles.
