Algebraic and Classical Topology. The Mathematical Works of by John Henry Constantine Whitehead PDF

By John Henry Constantine Whitehead

ISBN-10: 008009872X

ISBN-13: 9780080098722

Show description

Read or Download Algebraic and Classical Topology. The Mathematical Works of J. H. C. Whitehead PDF

Similar mathematics_1 books

Download PDF by Ian Doust, Brian Jefferies, Chun Li, Alan McIntosh (Eds.): Miniconference on Operators in Analysis, Macquarie

This quantity comprises the lawsuits of a 3 day miniconference on operator concept, partial differential equations, and similar parts of study, held at Macquarie collage, Sydney in September 1989, less than the sponsorship of the Centre for Mathematical research (Australian nationwide collage) whose monetary help is gratefully stated.

Download PDF by J.V.Narlikar - M.Narlikar: Fun and Fundamentals of Mathematics

This booklet introduces primary rules in arithmetic via intersting puzzles. scholars, from age12 upwards, who're uninterested in regimen classwork in maths will get pleasure from those puzzles on the way to sharpen will sharpen their logical reasoning. it truly is designed to arouse an curiosity in arithmetic between readers between readers within the 12-18 age staff.

Extra resources for Algebraic and Classical Topology. The Mathematical Works of J. H. C. Whitehead

Sample text

If B is a product bundle, then X(B) = 0, whence X(B) = 0. 11) in (9), it follows that E induces a homo­ morphism . 1\ u which is univalent if and only if E-i(0)cPiTn(S*). 4) _1 This will be the case, for example, if q = 3 or 7, for then £ (0) = 0, or iff n < 2q—2 (11). Since E oJ = —J o i* we have E*\(B) = —JX(B). 4) is satisfied. -P. Serre (12, p. 498) that 7rr(Sq) is finite except when r = q or when r = 2q— 1 and g is even. Since n > 1 it follows that An>(Z is finite if n ^ g. If n = g, then £ * is univalent and E* AniQ c 7r 2fl (^ +1 ), which is finite.

T Cf. 1) in (10). 1) HOMOTOPY THEORY OF SPHERE BUNDLES OVER SPHERES 45 Let n > 1 and, as in § 1, let pq: ir^RJ -+ 7rn_1(iJa) be the automorphism induced by the map r->pqrpqi where pqeOq is the reflection in the hyperplane tq_x = 0. 1) with T replaced by T. Let 0: F w x F f l - > F n x F « be defined by 0(y,z) = (y,pqz). Since Pq a* = a« and Pq T(y)uq z = T'{y)Pq uqz = T(y)uq Pq z it follows that pq o g = g' o 0. The map 0 is of degree — 1. 10 in (1) that pqij = £+Aa, for some a e 7rn(£«). 3) that (-t g ) o J£ = -Jpqi = -J£+Poc.

47 (1946), 779-85. 19. G. W. WHITEHEAD, A generalization of the Hopf invariant, Ann. , 51 (1950), 192-237. 20. G. W. WHITEHEAD, The (n -f 2)™* homotopy group of the n-sphere, Ann. , 52 (1950), 245-7. 21. G. W. WHITEHEAD, On the Freudenthal Theorems, Ann. , vol. 57 (1953), 209228. 22. J. H. C. WHITEHEAD, On adding relations to homotopy groups, Ann. , 42 (1941), 409-28. 23. J. H. C. WHITEHEAD, On the groups 7rr(F„, m) and sphere-bundles, Proc. London Math. Soc. (2), 48 (1944), 243-91. 24. J. H.

Download PDF sample

Algebraic and Classical Topology. The Mathematical Works of J. H. C. Whitehead by John Henry Constantine Whitehead


by Steven
4.0

Rated 4.57 of 5 – based on 32 votes