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E0互补问题的变形凝聚同伦算法     互补问题  凝聚函数  同伦算法  E0映射       font style='font-size:12px;'> 2014/1/8
利用变形凝聚函数构造同伦方程, 给出了同伦路径的存在性、 有界性及收敛性的构造性证明, 并利用数值算例验证了变形凝聚同伦算法求解互补问题可行、 有效.
On the existence of exotic homotopy 3-spheres      Homotopy spheres  3-manifold topology  Morse theory       font style='font-size:12px;'> 2011/1/17
This paper gives a geometric topological proof that exotic ho-motopy 3-spheres do not exist.
A topological defect separating a pair of two-dimensional CFTs is a codimension one interface along which all components of the stress-energy tensor glue continuously. We study topological defects of ...
For a smooth proper variety over a p-adic field, the Brauer group and abelian fundamental group are related to the higher Chow groups by the Brauer-Manin pairing and the class field theory. We general...
On H-groups and their applications to topological homotopy groups     H-group  sub-H-group  loop space  Topological homotopy       font style='font-size:12px;'> 2010/12/13
This paper develops a basic theory of H-groups. We intro-duce a special quotient of H-groups and extend some algebraic construc-tions of topological groups to the category of H-groups and H-maps. We u...
Tensor products of homotopy Gerstenhaber algebras      products  homotopy Gerstenhaber algebras        font style='font-size:12px;'> 2010/11/30
On the tensor product of two homotopy Gerstenhaber algebras we construct a Hirsch algebra structure which extends the canonical dg algebra structure. Our result applies more generally to tensor produc...
Bar-cobar duality for operads in stable homotopy theory      Bar-cobar duality  stable homotopy theory        font style='font-size:12px;'> 2010/12/13
We extend bar-cobar duality, defined for operads of chain complexes by Getzler and Jones, to operads of spectra in the sense of stable homotopy theory. Our main result is the existence of a Quillen e...
The homotopy theory of function spaces: A survey      Function space  monoid of self-equivalence  free loop space       font style='font-size:12px;'> 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...
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       font style='font-size:12px;'> 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          font style='font-size:12px;'> 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.
关于弱同伦扩张性质          font style='font-size:12px;'> 2007/12/12
D.Puppe在文[4]中提出了空间偶的弱同伦扩张性质(WHEP),这是经典的同伦扩张性质(HEP)概念的推广,它们在同伦论中都有重要的意义.本文的目的是讨论具有WHEP的空间偶的一系列性质. 本文的写作得到了周学光教授的鼓励,谨此表示感谢.

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