THE GEOMETRIC REALIZATION OF A SEMI-SIMPLICIAL COMPLEX
@article{Milnor1957THEGR, title={THE GEOMETRIC REALIZATION OF A SEMI-SIMPLICIAL COMPLEX}, author={John W. Milnor}, journal={Annals of Mathematics}, year={1957}, volume={65}, pages={357} }
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
273 Citations
On the notion of geometric realization
- Mathematics
- 2003
We explain why geometric realization commutes with Cartesian products and why the geometric realization of a simplicial set (resp. cyclic set) is equipped with an action of the group of orientation…
Commutative simplicial bundles
- Mathematics
- 2020
In this paper we introduce a simplicial analogue of principal bundles with commutativity structure and their classifying spaces defined for topological groups. Our construction is a variation of the…
An elementary illustrated introduction to simplicial sets
- Mathematics
- 2008
This is an expository introduction to simplicial sets and simplicial homotopy theory with particular focus on relating the combinatorial aspects of the theory to their geometric/topological origins.…
ON THE ADJUNCTION BETWEEN GEOMETRIC REALISATION AND SINGULAR SET
- Mathematics
- 2017
These are expository notes on simplicial sets. It contains a proof that geometric realisation of a simplicial set and singular set are adjoint functors; and that the full and diagonal realisation of…
Configurations, braids, and homotopy groups
- Mathematics
- 2005
The main results of this article are certain connections between braid groups and the homotopy groups of the 2-sphere. The connections are given in terms of Brunnian braids over the disk and over the…
Steenrod squares in signed simplicial sets
- Mathematics
- 2019
The cup-i products in semi-simplicial sets are developed following the work in [1]. The category of signed simplicial sets is presented, and using the cup-i product formulas, we find an operation in…
On the Geometry of 2-Categories and their Classifying Spaces
- Mathematics
- 2003
In this paper we prove that realizations of geometric nerves are classifying spaces for 2-categories. This result is particularized to strict monoidal categories and it is also used to obtain a…
References
SHOWING 1-10 OF 11 REFERENCES
On the realizability of homotopy groups and their operations
- Mathematics
- 1951
be a given sequence of abstract groups. All groups except the first one are abelian and additive, while 77£ is written multiplicatively. There are given two kinds of operations between these groups.…
ON THE EQUIVALENCE OF TWO SINGULAR HOMOLOGY THEORIES
- Mathematics
- 1950
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 Dowker…
Construction of Universal Bundles, II
- Philosophy
- 1956
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 and…
Relations between Homology and Homotopy Groups.
- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1943
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
Math. Soc
- Math. Soc
- 1949