## Combinatorial descriptions of the homotopy groups of certain spaces

Venue: | Math. Proc. Camb. Philos. Soc |

Citations: | 28 - 21 self |

### BibTeX

@ARTICLE{Wu_combinatorialdescriptions,

author = {Jie Wu},

title = {Combinatorial descriptions of the homotopy groups of certain spaces},

journal = {Math. Proc. Camb. Philos. Soc},

year = {},

pages = {489--513}

}

### OpenURL

### Abstract

Abstract. We give a combinatorial description of homotopy groups of ΣK(π, 1). In particular, all of the homotopy groups of the 3-sphere are combinatorially given. 1.

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Citation Context ... · , xj τ(m) ]. Definition 6.11. A simplicial group is minimal if it is also a minimal simplicial set. Recall that a simplicial group G is minimal if and only if the Moore chain complex NG is minimal =-=[C2]-=-. Theorem 6.12. The simplicial group K(S 1 ) is the universal minimal simplicial quotient simplicial group of F(S 1 ) in the following sense: (1). K(S 1 ) is a minimal simplicial group. (2). Let G be ... |

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