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1.
In this note we define fibrations of topological stacks and establish their main properties. When restricted to topological spaces, our notion of fibration coincides with the classical one. We prove various standard results about fibrations (long exact sequence for homotopy groups, Leray–Serre and Eilenberg–Moore spectral sequences, etc.). We prove various criteria for a morphism of topological stacks to be a fibration, and use these to produce examples of fibrations. We prove that every morphism of topological stacks factors through a fibration and construct the homotopy fiber of a morphism of topological stacks. As an immediate consequence of the machinery we develop, we also prove van Kampen?s theorem for fundamental groups of topological stacks. 相似文献
2.
Résumé. Etant donné un germe de morphisme analytique complexe à fibre réduite, nous étudions la manière dont la courbure de Lipschitz-Killing de la fibre de Milnor pour la métrique induite par celle de se concentre asymptotiquement, lorsque , dans l'intersection de cette fibre avec des boules dont les centres peuvent être décrits mais surtout dont les rayons sont de la forme où les des nombres rationnels dont la collection ne dépend que de la topologie du plongement dans du germe de courbe plane réduite .
Received: May 29, 1998. 相似文献
3.
Francesco Zucconi 《Transactions of the American Mathematical Society》2003,355(10):4045-4059
This article presents some results on the surfaces of general type whose Albanese morphism is a holomorphic fibre bundle.
4.
《Mathematische Nachrichten》2017,290(2-3):382-392
In this paper, we study the topology of real analytic map‐germs with isolated critical value , with . We compare the topology of f with the topology of the compositions , where are the projections , for . As a main result, we give necessary and sufficient conditions for f to have a Lê–Milnor fibration in the tube. 相似文献
5.
Takahisa Miyata 《Topology and its Applications》2010,157(14):2194-2224
The notions of pro-fibration and approximate pro-fibration for morphisms in the pro-category pro-Top of topological spaces were introduced by S. Mardeši? and T.B. Rushing. In this paper we introduce the notion of strong pro-fibration, which is a pro-fibration with some additional property, and the notion of ANR object in pro-Top, which is approximately an ANR-system, and we consider the full subcategory ANR of pro-Top whose objects are ANR objects. We prove that the category ANR satisfies most of the axioms for fibration category in the sense of H.J. Baues if fibrations are strong pro-fibrations and weak equivalences are morphisms inducing isomorphisms in the pro-homotopy category pro-H(Top) of topological spaces. We give various applications. First of all, we prove that every shape morphism is represented by a strong pro-fibration. Secondly, the fibre of a strong pro-fibration is well defined in the category ANR, and we obtain an isomorphism between the pro-homotopy groups of the base and total systems of a strong pro-fibration, and hence obtain the pro-homotopy sequence of a strong pro-fibration. Finally, we also show that there is a homotopy decomposition in the category ANR. 相似文献
6.
《代数通讯》2013,41(9):4611-4621
Abstract Let nand dbe natural integers satisfying n ≥ 3 and d ≥ 10. Let Xbe an irreducible real hypersurface Xin ? n of degree dhaving many pseudo-hyperplanes. Suppose that Xis not a projective cone. We show that the arrangement ? of all d ? 2 pseudo-hyperplanes of Xis trivial, i.e., there is a real projective linear subspace Lof ? n (?) of dimension n ? 2 such that L ? Hfor all H ∈ ?. As a consequence, the normalization of Xis fibered over ?1in quadrics. Both statements are in sharp contrast with the case n = 2; the first statement also shows that there is no Brusotti-type result for hypersurfaces in ? n , for n ≥ 3. 相似文献
7.
Chen Jixiang 《数学学报(英文版)》1998,14(3):321-326
K. A. Hardie and K. H. Kamps investigated the track homotopy categoryH
B
over a fixed spaceB ([1]). They have introduced two pairs of adjoint functors:P
B
N
B
andm
*
m
*, whereP
B
:H
B
→H
B
, andm
*:H
A
→H
B
for a fixed mapm:A→B. We have introduced a split fibration of categoriesL:H
b
→H
B
and provedL
J, J
L in [2]. This paper first extendsP
B
N
B
to
for any fixed mapb:
. Moreover we also extend these results to obtain two pairs of adjoint functors involving track homotopy categoriesH
b
andH
b
whereH
b
is the dual ofH
b
. One of our results isN
b
P
b
. This differs fromP
B
N
B
.
Supported by National Natural Science Foundation of China 相似文献
8.
Tang Mingyyuan 《东北数学》1994,(4)
Some New Combinatorial Conditions on the Singular Fibre of a FibrationTangMingyyuan(唐明元)(DepartmentofMathematics,ShanghaiNorm... 相似文献
9.
Mark Weber 《Applied Categorical Structures》2007,15(3):259-323
A 2-categorical generalisation of the notion of elementary topos is provided, and some of the properties of the Yoneda structure
(Street and Walters, J. Algebra, 50:350–379, 1978) it generates are explored. Results enabling one to exhibit objects as cocomplete in the sense definable within a Yoneda
structure are presented. Examples relevant to the globular approach to higher dimensional category theory are discussed. This
paper also contains some expository material on the theory of fibrations internal to a finitely complete 2-category (Street,
Lecture Notes in Math., 420:104–133, 1974) and provides a self-contained development of the necessary background material on Yoneda structures.
相似文献
10.
This paper takes up the systematic study of the Gottlieb groups of spheres for k≤13 by means of the classical homotopy theory methods. We fully determine the groups for k≤13 except for the 2-primary components in the cases: k=9,n=53;k=11,n=115. In particular, we show if n=2i−7 for i≥4. 相似文献