Whitehead torsion for PL fiber homotopy equivalences

1979 ◽  
pp. 90-101 ◽  
Author(s):  
Hans J. Munkholm
Keyword(s):  
Fiber Homotopy

On the Stable Homotopy Type of Thom Complexes

1973 ◽  
Vol 25 (6) ◽  
pp. 1285-1294 ◽  
Author(s):  
R. P. Held ◽  
D. Sjerve
Keyword(s):  
Vector Bundle ◽  
Homotopy Type ◽  
Stable Homotopy ◽  
Homotopy Equivalence ◽  
Real Vector ◽  
Fiber Homotopy

Let α be a real vector bundle over a finite CW complex X and let T(α;X) be its associated Thorn complex. We propose to study the S-type (stable homotopy type) of Thorn complexes in the framework of the Atiyah-Adams J-Theory. Therefore we focus our attention on the group JR(X) which is defined to be the group of orthogonal sphere bundles over X modulo stable fiber homotopy equivalence.

scholarly journals Two remarks on fiber homotopy type

1960 ◽  
Vol 10 (2) ◽  
pp. 585-590 ◽  
Author(s):  
John Milnor ◽  
Edwin Spanier
Keyword(s):  
Homotopy Type ◽  
Fiber Homotopy

On fiber homotopy equivalence

1959 ◽  
Vol 26 (4) ◽  
pp. 699-706 ◽  
Author(s):  
Edward Fadell
Keyword(s):  
Homotopy Equivalence ◽  
Fiber Homotopy

scholarly journals $G^{\infty}$-fiber homotopy equivalence

1989 ◽  
Vol 33 (4) ◽  
pp. 554-565
Author(s):  
S. Y. Husseini
Keyword(s):  
Homotopy Equivalence ◽  
Fiber Homotopy

A Generalization of Thom Classes and Characteristic Classes to Nonspherical Fibrations

1974 ◽  
Vol 26 (1) ◽  
pp. 138-144 ◽  
Author(s):  
Reinhard Schultz
Keyword(s):  
Homotopy Equivalent ◽  
Characteristic Classes ◽  
Contravariant Functor ◽  
Classifying Space ◽  
Topological Information ◽  
Homotopy Types ◽  
Universal Space ◽  
Special Cases ◽  
Topological Monoid ◽  
Fiber Homotopy

Let X be a polyhedron, and let Fx denote the contravariant functor consisting of fiber homotopy types of Hurewicz fibrations over a given base whose fibers are homotopy equivalent to X. A fundamental theorem on fiber spaces states that Fx is a representable homotopy functor and a universal space for Fx is the classifying space for the topological monoid of self-equivalences of X [2; 5]. Frequently, algebraic topological information about the associated universal fibration yields information about arbitrary fibrations with fiber (homotopy equivalent to) X. However, present knowledge of the algebraic topological properties of the universal base space is extremely limited except in some special cases.

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