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Links Not Concordant to the Hopf Link  [PDF]
Stefan Friedl,Mark Powell
Mathematics , 2011, DOI: 10.1017/S0305004114000036
Abstract: We give new Casson-Gordon style obstructions for a two-component link to be topologically concordant to the Hopf link.
On surface links whose link groups are abelian  [PDF]
Tetsuya Ito,Inasa Nakamura
Mathematics , 2013, DOI: 10.1017/S030500411400019X
Abstract: We study surface links whose link groups are free abelian, and construct various stimulating and highly non-trivial examples of such surface links.
Surface links with free abelian link groups  [PDF]
Inasa Nakamura
Mathematics , 2009, DOI: 10.2969/jmsj/06610247
Abstract: It is known that if a classical link group is a free abelian group, then its rank is at most two. It is also known that a $k$-component 2-link group ($k>1$) is not free abelian. In this paper, we give examples of $T^2$-links each of whose link groups is a free abelian group of rank three or four. Concerning the $T^2$-links of rank three, we determine the triple point numbers and we see that their link types are infinitely many.
Smooth concordance of links topologically concordant to the Hopf link  [PDF]
Jae Choon Cha,Taehee Kim,Daniel Ruberman,Saso Strle
Mathematics , 2010, DOI: 10.1112/blms/bdr103
Abstract: It was shown by Jim Davis that a 2-component link with Alexander polynomial one is topologically concordant to the Hopf link. In this paper, we show that there is a 2-component link with Alexander polynomial one that has unknotted components and is not smoothly concordant to the Hopf link, answering a question of Jim Davis. We construct infinitely many concordance classes of such links, and show that they have the stronger property of not being smoothly concordant to the Hopf link with knots tied in the components.
On the link Floer homology of $L$-space links  [PDF]
Nakul Dawra
Mathematics , 2015,
Abstract: We will prove that, for a $2$ or $3$ component $L$-space link, $HFL^-$ is completely determined by the multi-variable Alexander polynomial of all the sub-links of $L$, as well as the pairwise linking numbers of all the components of $L$. We will also give some restrictions on the multi-variable Alexander polynomial of an $L$-space link. Finally, we use the methods in this paper to prove a conjecture by Yajing Liu classifying all $2$-bridge $L$-space links.
Simplicial volume of links from link diagrams  [PDF]
Oliver Dasbach,Anastasiia Tsvietkova
Mathematics , 2015,
Abstract: The hyperbolic volume of a link complement is known to be unchanged when a half-twist is added to a link diagram, and a suitable 3-punctured sphere is present in the complement. We generalize this to the simplicial volume of link complements by analyzing the corresponding toroidal decompositions. We then use it to prove a refined upper bound for the volume in terms of twists of various lengths for links.
The missing links in the BGP-based AS connectivity maps  [PDF]
Shi Zhou,Raul J. Mondragon
Computer Science , 2003,
Abstract: A number of recent studies of the Internet topology at the autonomous systems level (AS graph) are based on the BGP-based AS connectivity maps (original maps). The so-called extended maps use additional data sources and contain more complete pictures of the AS graph. In this paper, we compare an original map, an extended map and a synthetic map generated by the Barabasi-Albert model. We examine the recently reported rich-club phenomenon, alternative routing paths and attack tolerance. We point out that the majority of the missing links of the original maps are the connecting links between rich nodes (nodes with large numbers of links) of the extended maps. We show that the missing links are relevant because links between rich nodes can be crucial for the network structure.
Geometric Residue Theorems for Bundle Maps  [PDF]
Sunil Nair
Mathematics , 1997,
Abstract: In this paper we prove geometric residue theorems for bundle maps over a compact manifold. The theory developed associates residues to the singularity submanifolds of the map for any invariant polynomial. The theory is then applied to a variety of settings: smooth maps between equidimensional manifolds, CR-singularities, finite singularities and singularities of odd forms as spinor bundle maps.
Multiplication maps and vanishing theorems for toric varieties  [PDF]
Osamu Fujino
Mathematics , 2006,
Abstract: We use multiplication maps to give a characteristic-free approach to vanishing theorems on toric varieties. Our approach is very elementary but is enough powerful to prove vanishing theorems.
Index theorems for holomorphic maps and foliations  [PDF]
Marco Abate,Filippo Bracci,Francesca Tovena
Mathematics , 2006,
Abstract: We describe a general construction providing index theorems localizing the Chern classes of the normal bundle of a subvariety inside a complex manifold. As particular instances of our construction we recover both Lehmann-Suwa's generalization of the classical Camacho-Sad index theorem for holomorphic foliations and our index theorem for holomorphic maps with positive dimensional fixed point set. Furthermore, we also obtain generalizations of recent index theorems of Camacho-Movasati-Sad and Camacho-Lehmann for holomorphic foliations transversal to a subvariety.
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