Maps from the minimal grope to an arbitrary grope

Matija Cencelj; Katsuya Eda; Aleš Vavpetič

doi:10.1142/S0218196713500070

Maps from the minimal grope to an arbitrary grope

Matija Cencelj^*, Katsuya Eda, Aleš Vavpetič

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We consider open infinite gropes and prove that every continuous map from the minimal grope to another grope is nulhomotopic unless the other grope has a «branch» which is a copy of the minimal grope. Since every grope is the classifying space of its fundamental group, the problem is translated to group theory and a suitable block cancellation of words is used to obtain the result.

Original language	English
Pages (from-to)	503-519
Number of pages	17
Journal	International Journal of Algebra and Computation
Volume	23
Issue number	3
DOIs	https://doi.org/10.1142/S0218196713500070
Publication status	Published - 2013 May

Keywords

Grope
perfect group

ASJC Scopus subject areas

Mathematics(all)

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10.1142/S0218196713500070

Cite this

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title = "Maps from the minimal grope to an arbitrary grope",

abstract = "We consider open infinite gropes and prove that every continuous map from the minimal grope to another grope is nulhomotopic unless the other grope has a «branch» which is a copy of the minimal grope. Since every grope is the classifying space of its fundamental group, the problem is translated to group theory and a suitable block cancellation of words is used to obtain the result.",

keywords = "Grope, perfect group",

author = "Matija Cencelj and Katsuya Eda and Ale{\v s} Vavpeti{\v c}",

year = "2013",

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T1 - Maps from the minimal grope to an arbitrary grope

AU - Cencelj, Matija

AU - Eda, Katsuya

AU - Vavpetič, Aleš

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Y1 - 2013/5

N2 - We consider open infinite gropes and prove that every continuous map from the minimal grope to another grope is nulhomotopic unless the other grope has a «branch» which is a copy of the minimal grope. Since every grope is the classifying space of its fundamental group, the problem is translated to group theory and a suitable block cancellation of words is used to obtain the result.

AB - We consider open infinite gropes and prove that every continuous map from the minimal grope to another grope is nulhomotopic unless the other grope has a «branch» which is a copy of the minimal grope. Since every grope is the classifying space of its fundamental group, the problem is translated to group theory and a suitable block cancellation of words is used to obtain the result.

KW - Grope

KW - perfect group

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ER -

Maps from the minimal grope to an arbitrary grope

Abstract

Keywords

ASJC Scopus subject areas

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