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2007 | 197 | 1 | 35-66
Tytu艂 artyku艂u

The homotopy dimension of codiscrete subsets of the 2-sphere 饾晩虏

Tre艣膰 / Zawarto艣膰
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Abstrakty
EN
Andreas Zastrow conjectured, and Cannon-Conner-Zastrow proved, that filling one hole in the Sierpi艅ski curve with a disk results in a planar Peano continuum that is not homotopy equivalent to a 1-dimensional set. Zastrow's example is the motivation for this paper, where we characterize those planar Peano continua that are homotopy equivalent to 1-dimensional sets. While many planar Peano continua are not homotopy equivalent to 1-dimensional compacta, we prove that each has fundamental group that embeds in the fundamental group of a 1-dimensional planar Peano continuum. We leave open the following question: Is a planar Peano continuum homotopically 1-dimensional if its fundamental group is isomorphic with the fundamental group of a 1-dimensional planar Peano continuum?
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autor
  • Department of Mathematics, Brigham Young University, Provo, UT 84602, U.S.A.
autor
  • Department of Mathematics, Brigham Young University, Provo, UT 84602, U.S.A.
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bwmeta1.element.bwnjournal-article-doi-10_4064-fm197-0-3
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