Groups of Homotopy Spheres: I

1963/05/01 by Michel Kervaire, John Milnor · 12 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Astronomy #Bott periodicity theorem #Homotopy #Homotopy and Cohomology in Algebraic Topology #Homotopy group #Homotopy sphere #Mathematics #Pure mathematics #SPHERES

paper · doi:10.2307/1970128

openalex publication_date 1963/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/18

Abstract

DEFINITION. Two closed n-manifolds M, and M2 are h-cobordant1 if the disjoint sum M, + (- M2) is the boundary of some manifold W, where both M1 and (-M2) are deformation retracts of W. It is clear that this is an equivalence relation. The connected sum of two connected n-manifolds is obtained by removing a small n-cell from each, and then pasting together the resulting boundaries. Details will be given in ? 2.

Citations

• Quelques propriétés globales des variétés différentiables
• A manifold which does not admit any differentiable structure
• Homologie Singuliere Des Espaces Fibres
• On Manifolds Homeomorphic to the 7-Sphere
• The Stable Homotopy of the Classical Groups
• Modifications and Cobounding Manifolds

Cited by

• Einstein metrics on spheres
• The Algebraic Theory of Surgery II. Applications to Topology
• Framed bordism of Lagrangian homotopy spheres via generating functions
• A secondary pairing between K-theory and K-homology, relative eta invariants, and zeta maps
• René Thom’s work on geometric homology and bordism
• Four-dimensional topology: an introduction
• On the obstructions to non-Cliffordian pin structures
• Compactification, topology change and surgery theory
• Foundations of algebraic surgery
• Exotic sphere [wikipedia]
• Homotopy groups of spheres [wikipedia]
• Surgery theory [wikipedia]