By Lynn Arthur Steen, J. Arthur Seebach Jr.
Over a hundred and forty examples, preceded by means of a succinct exposition of common topology and simple terminology. every one instance taken care of as an entire. Over 25 Venn diagrams and charts summarize homes of the examples, whereas discussions of basic tools of development and alter supply readers perception into developing counterexamples. comprises difficulties and workouts, correlated with examples. Bibliography.
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Extra info for Counterexamples in Topology (Dover Books on Mathematics)
C t) > 0 It1 > C (~(I~)) > C (i(zi)) > 0, denotes the c o c h i n complex of a graded Lie algebra. the isomorphism M(A~) ~ c (L(Z~)) which i s only formal, the cochain d i f f ~ e n t i a l terms of ~ DG-algebra~ pres~ves differentials. dc AM A~ For describes only the quadrate dM. The l-cochains u(i/j ) e M(I~), dual to the basis elements described earlier, are mapped to the cocycles relation in M(I£) z(i/j ) E Z£ c A%. 23) dMU(i/j ) = cic J shows that ~ coformal for has non-quadratic ~ > i. terms (for cj decomposable); The minimal algebras of the form hence C (L(Z%)) I~ is not have the homotopy type of a finite wedge of spheres, and their study goes back to P.
L(ii). Having now expressed our problem in terms of bordism theory we can translate it into homotopy theory. R. Wells  has shown that replacing embeddings by immersions in bordism theory corresponds to replacing homotopy groups of Thom complexes by their stable counterparts. e. is isomorphic to Sn+I(SI ) m Sn, the stable n-stem M0(1)) (S 1 = MS0(1)). 28 So the geometrical diagram SI (n,l) ~ e forget I orientatzon~ 6 ~ ~2 l ( n , l ) / / translates into homotopy theory as S ~ ~Sn+I(SI ) ~ n 2~2 ~+I (P~) 11 0 To study the problem using this diagram we must identify theoretically.
AMS 72 (1966), 358-428. groups for ~xG. 90 (1969), 226-234. Classification problems in topology IV (thickenings) Topology 5 (1966), 73-94. C. University Surgery on compact manifolds. of Warwick Coventry CV4 7AL, England Academic Press 1970. University of Geneva, Switzerland (current address) Homotopy invariants of foliations by S. Hurder and F. W. Kamber *) i. >.. A'(X), where I(G)£ ~, model [S]. G-structure on MA denote Let > 2£. DG-algebra A, The index £ depends on (X) = ~*(A'(X)) Sullivan-Dupont.