Algebraic TopologyIn most mathematics departments at major universities one of the three or four basic firstyear graduate courses is in the subject of algebraic topology. This introductory textbook in algebraic topology is suitable for use in a course or for selfstudy, featuring broad coverage of the subject and a readable exposition, with many examples and exercises. The four main chapters present the basic material of the subject: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature of the book is the inclusion of many optional topics which are not usually part of a first course due to time constraints, and for which elementary expositions are sometimes hard to find. Among these are: Bockstein and transfer homomorphisms, direct and inverse limits, Hspaces and Hopf algebras, the Brown representability theorem, the James reduced product, the DoldThom theorem, and a full exposition of Steenrod squares and powers. Researchers will also welcome this aspect of the book. 
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There are many texts available on Algebraic Topology. In my opinion, this is the book that provides geometric feeling to the readers including those seeing the subject for the first time.
Contents
II  ix 
III  1 
IV  4 
V  6 
VI  10 
VII  17 
IX  21 
X  25 
XLVIII  229 
XLIX  235 
L  245 
LI  248 
LII  257 
LIII  264 
LIV  277 
LV  288 
XI  30 
XII  36 
XIII  37 
XIV  39 
XV  46 
XVI  52 
XVII  56 
XVIII  59 
XIX  66 
XX  79 
XXI  83 
XXII  93 
XXIII  98 
XXIV  100 
XXV  104 
XXVI  106 
XXVII  109 
XXVIII  124 
XXIX  130 
XXX  133 
XXXI  145 
XXXII  149 
XXXIII  156 
XXXIV  158 
XXXV  162 
XXXVI  165 
XXXVII  173 
XXXVIII  181 
XL  186 
XLII  193 
XLIII  202 
XLIV  207 
XLV  214 
XLVI  220 
XLVII  226 
LVI  299 
LVII  307 
LVIII  317 
LIX  323 
LX  333 
LXI  335 
LXII  336 
LXIII  342 
LXIV  344 
LXV  348 
LXVI  356 
LXVIII  362 
LXIX  371 
LXX  380 
LXXI  389 
LXXII  401 
LXXIII  406 
LXXIV  411 
LXXV  417 
LXXVI  423 
LXXVII  425 
LXXVIII  427 
LXXIX  444 
LXXX  448 
LXXXI  452 
LXXXII  456 
LXXXIII  462 
LXXXIV  466 
LXXXV  471 
LXXXVI  483 
LXXXVII  515 
LXXXVIII  529 
535  
Common terms and phrases
abelian action algebra algebraic topology apply associated attaching basepoint basis boundary bundle called cell cellular chain complex circle closed coefficients cohomology commutative compact composition connected consider consisting construction contained continuous copies corresponding covering space cup product CW complex defined definition deformation retracts diagram dimension direct edges element example exercise extend fact factors fiber finite fixed formula fundamental given gives graph hence homology groups homomorphism homotopy equivalence identified identity implies inclusion induces injective isomorphism lift long exact sequence loop multiplication natural neighborhood obtained orientable pair path pathconnected polynomial preceding projection Proof Proposition prove quotient reduced relation relative represented restriction result ring says simplicial singular structure subcomplex subgroup subspace surjective suspension theorem theory topology trivial union unique universal vertices zero