000			01866 a2200241 4500
999			_c54758 _d54758
008			210323b ||||| |||| 00| 0 eng d
020			_a9780521055314
082			_a514.24 _bBAU
100			_aBaues, Hans Joachim
245			_aAlgebraic homotopy
260			_bCambridge University Press, _aCambridge: _c1988.
300			_axix, 466 p. : ill ; _bpb, _c24 cm.
365			_aGBP _b76.99
440			_aCambridge studies in advanced mathematics ; 15
504			_aIncludes index. Bibliography: p. [455]-460.
520			_aThis book gives a general outlook on homotopy theory; fundamental concepts, such as homotopy groups and spectral sequences, are developed from a few axioms and are thus available in a broad variety of contexts. Many examples and applications in topology and algebra are discussed, including an introduction to rational homotopy theory in terms of both differential Lie algebras and De Rham algebras. The author describes powerful tools for homotopy classification problems, particularly for the classification of homotopy types and for the computation of the group homotopy equivalences. Applications and examples of such computations are given, including when the fundamental group is non-trivial. Moreover, the deep connection between the homotopy classification problems and the cohomology theory of small categories is demonstrated. The prerequisites of the book are few: elementary topology and algebra. Consequently, this account will be valuable for non-specialists and experts alike. It is an important supplement to the standard presentations of algebraic topology, homotopy theory, category theory and homological algebra.
650			_acofibration categories
650			_aCategories (Mathematics)
650			_aHomotopy theory
650			_aCW-complexes
650			_aHomotopy theory of Postnikov towers
942			_2ddc _cTD