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Homotopy type of planar Peano continua
Advances in Mathematics ( IF 1.7 ) Pub Date : 2021-08-27 , DOI: 10.1016/j.aim.2021.107971 Curtis Kent
中文翻译:
平面Peano连续体的同伦型
更新日期:2021-08-27
Advances in Mathematics ( IF 1.7 ) Pub Date : 2021-08-27 , DOI: 10.1016/j.aim.2021.107971 Curtis Kent
We prove that the homotopy equivalence class of a map from a Peano continuum into a planar or one-dimensional Peano continuum is determined by the induced homomorphism of fundamental groups. This provides a new proof that planar sets are aspherical and is used to prove that two planar or one-dimensional Peano continua are homotopy equivalent if and only if they have isomorphic fundamental groups.
中文翻译:
平面Peano连续体的同伦型
我们证明了从皮亚诺连续统到平面或一维皮亚诺连续统的映射的同伦等价类是由基本群的诱导同态决定的。这提供了平面集是非球面的新证明,并用于证明两个平面或一维皮亚诺连续体是同伦等价的,当且仅当它们具有同构基本群。