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Francois Laudenbach
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Given a Morse function f on a closed manifold M with distinct critical values, and given a field F, there is a canonical complex, called the Morse-Barannikov complex, which is equivalent to any Morse complex associated with f and whose form is simple. In particular, the homology of M with coefficients in F is immediately readable on this complex. The bifurcation theory of this complex in a generic one-parameter family of functions will be investigated. Applications to the boundary manifolds will be given.
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We apply Lescops construction of $mathbb{Z}$-equivariant perturbative invariant of knots and 3-manifolds to the explicit equivariant propagator of AL-paths given in arXiv:1403.8030. We obtain an invariant $hat{Z}_n$ of certain equivalence classes of fiberwise Morse functions on a 3-manifold fibered over $S^1$, which can be considered as a higher loop analogue of the Lefschetz zeta function and whose construction will be applied to that of finite type invariants of knots in such a 3-manifold. We also give a combinatorial formula for Lescops equivariant invariant $mathscr{Q}$ for 3-manifolds with $H_1=mathbb{Z}$ fibered over $S^1$. Moreover, surgery formulas of $hat{Z}_n$ and $mathscr{Q}$ for alternating sums of surgeries are given. This gives another proof of Lescops surgery formula of $mathscr{Q}$ for special kind of 3-manifolds and surgeries, which is simple in the sense that the formula is obtained easily by counting certain graphs in a 3-manifold.
In order to better understand the effect of social media in the dissemination of scholarly articles, employing the daily updated referral data of 110 PeerJ articles collected over a period of 345 days, we analyze the relationship between social media attention and article visitors directed by social media. Our results show that social media presence of PeerJ articles is high. About 68.18% of the papers receive at least one tweet from Twitter accounts other than @PeerJ, the official account of the journal. Social media attention increases the dissemination of scholarly articles. Altmetrics could not only act as the complement of traditional citation measures but also play an important role in increasing the article downloads and promoting the impacts of scholarly articles. There also exists a significant correlation among the online attention from different social media platforms. Articles with more Facebook shares tend to get more tweets. The temporal trends show that social attention comes immediately following publication but does not last long, so do the social media directed article views.
We show that any 4-manifold admitting a $(g;k_1,k_2,0)$-trisection is an irregular 3-fold cover of the 4-sphere whose branching set is a surface in $S^4$, smoothly embedded except for one singular point which is the cone on a link. A 4-manifold admits such a trisection if and only if it has a handle decomposition with no 1-handles; it is conjectured that all simply-connected 4-manifolds have this property.
Let $k$ be a subring of the field of rational functions in $x, v, s$ which contains $x^{pm 1}, v^{pm 1}, s^{pm 1}$. If $M$ is an oriented 3-manifold, let $S(M)$ denote the Homflypt skein module of $M$ over $k$. This is the free $k$-module generated by isotopy classes of framed oriented links in $M$ quotiented by the Homflypt skein relations: (1) $x^{-1}L_{+}-xL_{-}=(s-s^{-1})L_{0}$; (2) $L$ with a positive twist $=(xv^{-1})L$; (3) $Lsqcup O=(frac{v-v^{-1}}{s-s^{-1}})L$ where $O$ is the unknot. We give two bases for the relative Homflypt skein module of the solid torus with 2 points in the boundary. The first basis is related to the basis of $S(S^1times D^2)$ given by V. Turaev and also J. Hoste and M. Kidwell; the second basis is related to a Young idempotent basis for $S(S^1times D^2)$ based on the work of A. Aiston, H. Morton and C. Blanchet. We prove that if the elements $s^{2n}-1$, for $n$ a nonzero integer, and the elements $s^{2m}-v^{2}$, for any integer $m$, are invertible in $k$, then $S(S^{1} times S^2)=k$-torsion module $oplus k$. Here the free part is generated by the empty link $phi$. In addition, if the elements $s^{2m}-v^{4}$, for $m$ an integer, are invertible in $k$, then $S(S^{1} times S^2)$ has no torsion. We also obtain some results for more general $k$.
Scholarly article impact reflects the significance of academic output recognised by academic peers, and it often plays a crucial role in assessing the scientific achievements of researchers, teams, institutions and countries. It is also used for addressing various needs in the academic and scientific arena, such as recruitment decisions, promotions, and funding allocations. This article provides a comprehensive review of recent progresses related to article impact assessment and prediction. The~review starts by sharing some insight into the article impact research and outlines current research status. Some core methods and recent progress are presented to outline how article impact metrics and prediction have evolved to consider integrating multiple networks. Key techniques, including statistical analysis, machine learning, data mining and network science, are discussed. In particular, we highlight important applications of each technique in article impact research. Subsequently, we discuss the open issues and challenges of article impact research. At the same time, this review points out some important research directions, including article impact evaluation by considering Conflict of Interest, time and location information, various distributions of scholarly entities, and rising stars.
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