Homotopy type of mapping spaces and existence of geometric exponents
Homotopy type of mapping spaces and existence of geometric exponents
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映射空间的同伦型与几何指数的存在性
DOI：
10.1515/forum.2010.024
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
J. Smrekar
中科院分区：
文献类型：
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作者：
J. Smrekar
设Y是单连通有限复数，p是素数。设Sm[p-1]表示由m-球面反p得到的复数.本文证明了Y在p处有最终H-空间指数当且仅当点映射Sm[p-1]→Y的空间映射*(Sm[p-1]，Y)对某些(因而都足够大)m具有CW复形的同伦型.这使得用映射空间的幻象来解释最终H-空间指数问题成为可能.
Abstract Let Y be a simply connected finite complex and let p be a prime. Let Sm [p –1] denote the complex obtained from the m-sphere by inverting p. It is shown in this paper that Y has an eventual H-space exponent at p if and only if the space map*(Sm [p –1], Y) of pointed maps Sm [p –1] → Y has the homotopy type of a CW complex for some (and hence all big enough) m. This makes it possible to interpret the question of eventual H-space exponents in terms of phantom phenomena of mapping spaces.