Positive weights and self-maps. (English) Zbl 1503.55009
There are many spaces that have positive weights, for example, formal spaces, homogeneous spaces and smooth complex algebraic varieties are spaces that have positive weights. A simply connected space has positive weights if its Sullivan minimal algebra has a family, parametrized over the rationals, of endomorphisms that, basically, rescale the generators of the algebra (see the paper for technical details and other equivalent definitions). These homomorphisms of course induce self maps in the rationalization of the space. In this short paper the author proves that if a finite simply connected CW-complex has positive weights then we can select in the family parametrized over the rationals of self maps of the rationalization of the finite complex, a subfamily parametrized over the integers that can be realized as self maps of the finite CW-complex. The author also gives some aplications of this result and relates it with similar previous results in the literature.
Reviewer: Antonio Garvin (Málaga)
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