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For any -complexes and , we show that . We use this fact to compute generalized evaluation subgroups of generalized tori relative to a sphere.
4.
Zbigniew Jelonek 《Proceedings of the American Mathematical Society》2003,131(5):1361-1367
Let be a polynomial of degree . Assume that the set there is a sequence s.t. and is finite. We prove that the set of generalized critical values of (hence in particular the set of bifurcation points of ) has at most points. Moreover, We also compute the set effectively.
5.
Fibrators help detect approximate fibrations. A closed, connected -manifold is called a codimension-2 fibrator if each map defined on an -manifold such that all fibre , are shape equivalent to is an approximate fibration. The most natural objects to study are s-Hopfian manifolds. In this note we give some necessary and sufficient conditions for s-Hopfian manifolds to be codimension-2 fibrators.
6.
Dominique Bourn 《Applied Categorical Structures》2000,8(1-2):81-113
Given a left exact category B, the construction of the nerve functor
n
for n-groupoids in B is related to a certain property of the category S-S i m p l
n – 1
B of the split (n – 1)-truncated simplicial objects in B, which allows us to define the split n-truncated simplicial objects in B completely internally to S-S i m p l
n – 1
B and thus to construct intrisincally from it the category S-S i m p l
n
B. 相似文献
7.
Toshihiro Yamaguchi 《Czechoslovak Mathematical Journal》2005,55(4):997-1001
We give an example of a space X with the property that every orientable fibration with the fiber X is rationally totally non-cohomologous to zero, while there exists a nontrivial derivation of the rational cohomology of
X of negative degree. 相似文献
8.
C. Weibel 《Selecta Mathematica, New Series》2001,7(4):533-564
No Abstract. 相似文献
9.
10.
R. W. Kieboom 《Applied Categorical Structures》1997,5(2):131-142
It is well known that the concept of monomorphism in a category can be defined using an appropriate pullback diagram. In the homotopy category of TOP pullbacks do not generally exist. This motivated Michael Mather to introduce another notion of homotopy pullback which does exist. The aim of this paper is to investigate the modified notion of homotopy monomorphism obtained by applying the pullback characterization using Mather's homotopy pullback. The main result of Section 1 shows that these modified homotopy monomorphisms are exactly those homotopy monomorphisms (in the usual sense) which are homotopy pullback stable, hence the terminology “stable” homotopy monomorphism. We also link these stable homotopy monomorphisms to monomorphisms and products in the track homotopy category over a fixed space. In Section 2 we answer the question: when is a (weak) fibration also a stable homotopy monomorphism? In the final section it is shown that the class of (weak) fibrations with this additional property coincides with the class of “double” (weak) fibrations. The double (weak) covering homotopy property being introduced here is a stronger version of the (W) CHP in which the final maps of the homotopies involved play the same role as the initial maps. 相似文献