arXiv subjects

Roman Golovko

Publications and source records attributed to Roman Golovko.

24 records · Page 2Linked to original sources

arXiv2015

Floer homology and Lagrangian concordance

We derive constraints on Lagrangian concordances from Legendrian submanifolds of the standard contact sphere admitting exact Lagrangian fillings. More precisely, we show that such a concordance induces an isomorphism on the level of bilinearised Legendrian contact cohomology. This is used to prove the existence of non-invertible exact Lagrangian concordances in all dimensions. In addition, using a result of Eliashberg-Polterovich, we completely classify exact Lagrangian concordances from the Legendrian unknot to itself in the tight contact-three sphere: every such concordance is the trace of a Legendrian isotopy. We also discuss a high dimensional topological result related to this classification.

math.SG↗

arXiv2014

On homological rigidity and flexibility of exact Lagrangian endocobordisms

We show that an exact Lagrangian cobordism $L\subset \mathbb R \times P \times \mathbb R$ from a Legendrian submanifold $Λ\subset P\times \mathbb R$ to itself satisfies $H_i(L;\mathbb F)=H_i(Λ;\mathbb F)$ for any field $\mathbb F$ in the case when $Λ$ admits a spin exact Lagrangian filling and the concatenation of any spin exact Lagrangian filling of $Λ$ and $L$ is also spin. The main tool used is Seidel's isomorphism in wrapped Floer homology. In contrast to that, for loose Legendrian submanifolds of $\mathbb{C}^n \times \mathbb R$, we construct examples of such cobordisms whose homology groups have arbitrary high ranks. In addition, we prove that the front $S^m$-spinning construction preserves looseness, which implies certain forgetfulness properties of it.

math.SG↗

arXiv2014

The cylindrical contact homology of universally tight sutured contact solid tori

We calculate the sutured version of cylindrical contact homology of a sutured contact solid torus $(S^1\times D^2,Γ, ξ)$, where $Γ$ consists of $2n$ parallel sutures of arbitrary slope and $ξ$ is a universally tight contact structure. In particular, we show that it is non-zero. This computation is one of the first computations of the sutured version of cylindrical contact homology and does not follow from computations in the closed case.

math.SG↗

arXiv2013

A note on the front spinning construction

In this paper we introduce a notion of front S^m-spinning for Legendrian submanifolds of R^{2n+1}. It generalizes the notion of front S^1-spinning which was invented by Ekholm, Etnyre and Sullivan. We use it to prove that there are infinitely many pairs of exact Lagrangian cobordant and not pairwise Legendrian isotopic Legendrian S^1 x S^{i_1} x ... x S^{i_k} in the standard contact Euclidean space which have the same classical invariants if one of i_j's is odd.

math.SG↗

arXiv2012

A note on Lagrangian cobordisms between Legendrian submanifolds of R^{2n+1}

We study the relation of an embedded Lagrangian cobordism between two closed, orientable Legendrian submanifolds of R^{2n+1}. More precisely, we investigate the behavior of the Thurston-Bennequin number and (linearized) Legendrian contact homology under this relation. The result about the Thurston-Bennequin number can be considered as a generalization of the result of Chantraine which holds when n = 1. In addition, we provide a few constructions of Lagrangian cobordisms and prove that there are infinitely many pairs of exact Lagrangian cobordant and not pairwise Legendrian isotopic Legendrian n-tori in R^{2n+1}.

math.SG↗

arXiv2011

The embedded contact homology of sutured solid tori

We calculate the relative versions of embedded contact homology, contact homology and cylindrical contact homology of the sutured solid torus $(S^1\times D^2,Γ)$, where $Γ$ consists of $2n$ parallel longitudinal sutures.

math.SG↗