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Maria Rita Casali 《Annali dell'Universita di Ferrara》1987,33(1):247-258
Summary Given a knotK⊂S
3, it is known a standard method for constructing a 4-coloured graph representing the closed orientable 3-manifoldM=M(K, d, ω) which is thed-fold covering space ofS
3 branched overK and associated to the transitived-representation ω of the knot group.
In this paper we obtain a presentation of the fundamental group ofM, directly from the Wirtinger presentation of the knot group and from the transitived-representation ω.
Work performed under the auspicies of the G.N.S.A.G.A. of the C.N.R. (National Research Council of Italy) and financially supported by M.P.I. (project ?Geometria delle Varietà differenziabili?). 相似文献
Riassunto Dato un nodoK⊂S 3, è noto un metodo standard per costruire un grafo 4-colorato rappresentante la 3-varietà chiusa ed orientabileM=M(K, d, ω) che è lo spazio di rivestimento diS 3 ramificato suK ed associato allad-rappresentazione transitiva ω del gruppo del nodo. In questo articolo si ottiene una presentazione del gruppo fondamentale diM, direttamente dalla presentazione di Wirtinger del gruppo del nodo e dallad-rappresentazione transitiva ω.
Work performed under the auspicies of the G.N.S.A.G.A. of the C.N.R. (National Research Council of Italy) and financially supported by M.P.I. (project ?Geometria delle Varietà differenziabili?). 相似文献
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James F. Davis 《Mathematische Annalen》1995,301(1):507-518
Partially supported by NSF grant DMS-9208052 and the MSRI NSF grant DMS-9022140. The author held an MSRI Research Professorship while the paper was being written 相似文献
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James F. Davis 《Mathematische Annalen》1995,301(1):519-528
Partially supported by NSF grant DMS-9208052 and the MSRI NSF grant DMS-9022140. The author held an MSRI Research Professorship while the paper was being written 相似文献
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In this note, we show that a monotonically normal space that is monotonically countably metacompact (monotonically meta-Lindelöf) must be hereditarily paracompact. This answers a question of H.R. Bennett, K.P. Hart and D.J. Lutzer. We also show that any compact monotonically meta-Lindelöf T2-space is first countable. In the last part of the note, we point out that there is a gap in Proposition 3.8 which appears in [H.R. Bennett, K.P. Hart, D.J. Lutzer, A note on monotonically metacompact spaces, Topology Appl. 157 (2) (2010) 456-465]. We finally give a detailed proof of how to overcome the gap. 相似文献
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Sławomir Cynk 《Mathematische Zeitschrift》2002,240(4):731-743
In this paper we study the Hodge numbers of a branched double covering of a smooth, complete algebraic threefold. The involution
on the double covering gives a splitting of the Hodge groups into symmetric and skew-symmetric parts. Since the symmetric
part is naturally isomorphic to the corresponding Hodge group of the base we study only the skew-symmetric parts and prove
that in many cases it can be computed explicitly.
Received: 6 March 2001 / in final form: 4 September 2001/ Published online: 4 April 2002 相似文献
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In this note we introduce and analyze maximal covering location games. As the core may be empty, several sufficient conditions for core non-emptiness are presented. For each condition we provide an example showing that when the condition is not satisfied, core non-emptiness is not guaranteed. 相似文献
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讨论csf可数空间的性质,把csf可数空间刻画为度量空间的映像,同时探讨了伪紧的csf可数空间的第一可数性质,推广了Arhangel’skiˇ?关于度量空间伪开s映像的结果,证明了正则伪紧的仿拓扑群是可度量化的当且仅当它是csf可数的Fr′echet空间. 相似文献
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Otte Hustad 《Israel Journal of Mathematics》1973,16(1):117-119
For a family of closed balls in a normed space we define the concept of weak intersection property, and we show that a complex
Banch space is a
space if and only if every family of closed balls with the weak intersection property has a non-empty intersection. 相似文献
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Marco Reni 《Mathematische Annalen》2000,316(4):681-697
We consider the following problem from the Kirby's list (Problem 3.25): Let K be a knot in and M(K) its 2-fold branched covering space. Describe the equivalence class [K] of K in the set of knots under the equivalence relation if is homeomorphic to . It is known that there exist arbitrarily many different hyperbolic knots with the same 2-fold branched coverings, due to
mutation along Conway spheres. Thus the most basic class of knots to investigate are knots which do not admit Conway spheres.
In this paper we solve the above problem for knots which do not admit Conway spheres, in the following sense: we give upper
bounds for the number of knots in the equivalence class [K] of a knot K and we describe how the different knots in the equivalence class of K are related.
Received: 3 August 1998 / in final form: 17 June 1999 相似文献
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Muammer Kula 《Acta Mathematica Hungarica》2011,133(1-2):14-32
In previous papers, various notions of (strongly) closed subobject, (strongly) open subobject, connected, compact and T i , i=0,1,2 objects in a topological category were introduced and compared. The main objective of this paper is to characterize each of these classes of objects in the category of Cauchy spaces as well as to examine how these generalizations are related. 相似文献
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In a recent paper [3], D. Buhagiar and B. A. Pasynkov introduced the notion of a supercomplete space and established an internal
characterization of these spaces. It is clear that the proof of this characterization actually characterizes c--supercomplete spaces. In this short note we state the correct formulation and give a counterexample.
Supported in part by the NSFC (No. 10571151, 10671173). 相似文献