A construction of a CW-decomposition of s-cubes which are manifolds. (English) Zbl 0617.57014

Tvarožek, Jozef

Math. Slovaca 36, 245-252 (1986).

In the paper by M. Božek and the author [Acta Math. Univ. Comenianae 46/47, 7-11 (1985; see the preceding review)] a CW- decomposition \({\mathcal F}^ n\) of the n-dimensional cube \(I^ n\) is introduced in such a way that for any given s-cube \(X=I^ n/(u^ 1,...,u^ n)\) the equivalence relation T is a cellular one on the CW- space \((I^ n, {\mathcal F}^ n)\), and a CW-decomposition \({\mathcal F}^ n/T\) of \(I^ n/T\) is constructed. In the present paper a construction of a simpler CW-decomposition \({\mathcal H}\) of those s-cubes which are manifolds is given. The number of cells of \({\mathcal H}\) is much smaller than that of \({\mathcal F}^ n\).

MSC:

57N99	Topological manifolds
54B15	Quotient spaces, decompositions in general topology
57Q05	General topology of complexes

Keywords:

quotient space of cube; CW-decomposition; s-cubes which are manifolds

Citations:

Zbl 0617.57013; Zbl 0591.57014

References:

[1]	BOŽEK M., TVAROŻEK J.: CW-decompositions and orientability of s-cubes. · Zbl 0617.57013
[2]	DOLD A.: Lectures on Algebraic Topology. Springer Verlag, Berlin 1972. · Zbl 0234.55001
[3]	LUNDELL A. T., WEINGRAM S.: The Topology of CW Complexes. Van Nostrand Reinhold Company, New York 1969. · Zbl 0207.21704
[4]	TVAROŽEK J.: s-cubes. Math. Slovaca 36, 1986, 55-68 · Zbl 0617.57014