Decompositions of Manifolds
Decomposition theory studies decompositions, or partitions, of manifolds into simple pieces, usually cell-like sets. Since its inception in 1929, the subject has become an important tool in geometric topology. The main goal of the book is to help students interested in geometric topology to bridge the gap between entry-level graduate courses and research at the frontier as well as to demonstrate interrelations of decomposition theory with other parts of geometric topology. With numerous exercises and problems, many of them quite challenging, the book continues to be strongly recommended to everyone who is interested in this subject. The book also contains an extensive bibliography and a useful index of key words, so it can also serve as a reference to a specialist.
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0-dimensional 1-LCC embedded argument bicollared Bing Cantor set cell-like decomposition cell-like map cell-like subset cellular decomposition cellularity criterion closed subset compact metric space compact subset component connected construction contains contractible Corollary 3A countable decom decomposition map decomposition space diam diameter less E"+l elements of G embedding dimension equivalent Example Exercise exists a homeomorphism finite finite-dimensional g e G G is shrinkable G-saturated open cover given grope Hausdorff space homeo homeomorphism homotopy hypothesis implies induced integer intersect l)-sphere Lemma locally compact manifold map F mapping cylinder metric space morphism n-cell n-manifold nondegenerate elements nonshrinkable null sequence obtain open cover open set open subset pairwise disjoint PL n-manifold prove regular neighborhood result retract satisfies the cellularity Section shrinkable decomposition shrinking simplex simplicial solid torus starlike strongly shrinkable Suppose G topology trivial upper semicontinuous
Page 311 - JHC Whitehead, Simplicial spaces, nuclei and m-groups, Proc. London Math. Soc. 45 (1939), 243-327, (Math.
Page 303 - Sur l'homeomorphie de deux figures et de leurs voisinages, J. Math. Pures. Appl., 86 (1921), 221-235.
Page 303 - Jersey, 1966.  Homotopy properties of decomposition spaces. Trans. Amer. Math. Soc. 143 (1969), 499-507.
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