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The homotopy theory of function spaces: A survey
Function space monoid of self-equivalence free loop space
2010/11/30
We survey research on the homotopy theory of the space map(X, Y )consisting of all continuous functions between two topological spaces. We summarize progress on various classification problems for the...
Higher topological complexity and homotopy dimension of configuration spaces on spheres
Lusternik-Schnirelmann category Schwarz genus topological complexity configuration spaces hyperplane arrangements
2010/12/3
In the paper “On Higher Analogs of Topological Complexity”Yu. Rudyak introduced the concept of TCn(X), the nth topological complexity of a path-connected space X. This concept was developed as a gener...
关于同伦满态与覆叠空间
同伦满态 同伦推出 覆叠空间 升腾
2007/12/12
本文在点标道路连通CW空间的同伦范畴中，利用同伦推出示性了同伦满态，得出了若$f:X\rightarrowY$是同伦满态，则对$\pi_1Y$的任一正规子群H，升腾映射$\tilde{f}:\tilde{X}_{(f_\#^{-1})}\rightarrow\tilde{Y}_{(H)}$也是同伦满态．
关于链同伦前伸的注记
2007/12/12
首先,本文在链复形和链映射范畴dA中证明了各种同伦扩张性质(HEP,WHEP,RWHEP与VWHEP)是等价的.这不同于拓扑空间和连续映射范畴Top.其次,在范踌dA中也有Puppe序列,本文证明了约化奇异链函子保持Puppe序列的右正合性.最后,与范畴Top相类似,在链同伦前伸方块中一个链同伦等价诱导出另一个链同伦等价.