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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.
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
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
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 admit
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 b
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 addr