THE GEOMETRIC REALIZATION OF A SEMI-SIMPLICIAL COMPLEX

@article{Milnor1957THEGR,
  title={THE GEOMETRIC REALIZATION OF A SEMI-SIMPLICIAL COMPLEX},
  author={J. Milnor},
  journal={Annals of Mathematics},
  year={1957},
  volume={65},
  pages={357}
}
  • J. Milnor
  • Published 1957
  • Mathematics
  • Annals of Mathematics
homology and homotopy groups. The terminology for semi-simplicial complexes will follow John Moore [7]. In particular the face and degeneracy maps of K will be denoted by d: Kn Kn-1 and si:K. -> Kn+1 respectively. 1. The definition 
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References

SHOWING 1-10 OF 13 REFERENCES
ON THE EQUIVALENCE OF TWO SINGULAR HOMOLOGY THEORIES
Eilenberg in 1944 ([E])2 removed some of the difficulties associated with the classical concept of "singular cell" and obtained a new singular homology theory. In 1948, Hurewicz, Dugundji, and DowkerExpand
Construction of Universal Bundles, II
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology andExpand
Construction of universal bundles I , Ann. of hlath
  • Construction of universal bundles I , Ann. of hlath
  • 1956
From Lemmas 5 and G it can be proved, using a relative Hurewica theorem, that the honlomorphisms are isomorphisms for all n . (The proof of the relative EIuren-icz theorem
  • Ann. of hlath,
  • 1950
ZILBER, Semi-simplicial complexes and singular homology, Ann
  • Ann. of hlath.,
  • 1950
Math. Soc
  • Math. Soc
  • 1949
...
1
2
...