A Theorem of Van Kampen Type for Pseudo Peano Continuum Spaces

Hanieh Mirebrahimi; Behrooz Mashayekhy

A Theorem of Van Kampen Type for Pseudo Peano Continuum Spaces

Algebraic Topology 2011-03-10 v1

Authors: Hanieh Mirebrahimi , Behrooz Mashayekhy

Abstract

G. Conner and K. Eda (Topology and its Applications, 146, (2005), 317-328.) introduced a new construction of spaces from groups. They remarked that the construction is not categorical. In this paper, based on the work of Conner and Eda, we construct two new categories for which the functor of the fundamental group $\pi$ has a right adjoint and consequently is right exact and preseves direct limits. Also, we study the behavior of the functor $\pi$ on quotient spaces and give a new version of Van Kampen theorem for join of spaces in the new categories.

Keywords

Van Kampen theorem fundamental group adjoint functor pseudo Peano continuum quotient space join of spaces categorical construction

Cite

@article{arxiv.1103.1738,
  title  = {A Theorem of Van Kampen Type for Pseudo Peano Continuum Spaces},
  author = {Hanieh Mirebrahimi and Behrooz Mashayekhy},
  journal= {arXiv preprint arXiv:1103.1738},
  year   = {2011}
}

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16 pages

A Theorem of Van Kampen Type for Pseudo Peano Continuum Spaces

Abstract

Keywords

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