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Marián Poppr

Publications and source records attributed to Marián Poppr.

2 recordsLinked to original sources
arXiv2026

A cord algebra for tori in three-space

Given a thin torus $T_K$ around a knot $K\subset \mathbb{R}^3$, we construct Morse models of cord algebra $Cord(T_K)$ with $\mathbb{Z}$ and loop space coefficients. Using the Multiple time scale dynamics we identify $Cord(T_K; \mathbb{Z})$ with $Cord(K; \mathbb{Z})$. In combination with the works of Cieliebak-Ekholm-Latschev-Ng and Petrak this indirectly relates $Cord(T_K)$ to $0$-th degree Legendrian contact homology $LCH_0(\mathcal{L}^\ast_+ T_K)$ of one component of the unit conormal bundle over $T_K$. Our definition of $Cord(T_K)$ is motivated by $J$-holomorphic curves with boundary on the Lagrangian submanifold $L^\ast_+ T_K\cup\mathbb{R}^3$ with an arboreal singularity along the torus $T_K$.

math.SG↗
arXiv2026

Non-contractible loops of Legendrian tori from families of knots

In the unit cotangent bundle of $\mathbb{R}^3$, we consider loops of Legendrian tori arising as families of the unit conormal bundles of smooth knots in $\mathbb{R}^3$. In this paper, using the cord algebra of knots, we give a topological method to compute the monodromy on the Legendrian contact homology in degree $0$ induced by those loops. As an application, we obtain an infinite family of non-contractible loops of Legendrian tori which are contractible in the space of smoothly embedded tori.

math.SG↗