arXiv subjects

Arun Maiti

Publications and source records attributed to Arun Maiti.

7 recordsLinked to original sources

arXiv2026

Unboundedness of the Heesch Number for Hyperbolic Convex Monotiles

A homogeneous (also known as semi-regular) tiling is an edge-to-edge tiling by regular polygons in which every vertex has the same cyclic type. We resolve the Heesch problem in the hyperbolic plane both for such tilings and for convex monotiles, in the latter case without any edge-to-edge restriction. We also construct an infinite family of weakly aperiodic convex monotiles whose interior angles are rational multiples of $\pi$.

math.CO↗

arXiv2024

The mod-2 cohomology groups of low-dimensional unordered flag manifolds and Auerbach bases

Unordered flag manifolds are the manifolds of unordered $n$-tuple of mutually orthogonal lines in $\mathbb{R}^n$. In this paper, we develop some basic tools to compute the mod-$2$ cohomology groups of these spaces, and apply them for explicit computation for small $n$. We show that this computation improves the known estimate of the number of Auerbach bases of normed linear spaces of small dimensions.

math.AT↗

arXiv2023

A Morse theoretic description of the Goresky-Hingston product

The Goresky-Hingston coproduct was first introduced by D. Sullivan and later extended by M. Goresky and N. Hingston. In this article we give a Morse theoretic description of the coproduct. Using the description we prove homotopy invariance property of the coproduct. We describe a connection between our Morse theoretic coproduct and a coproduct on Floer homology of cotangent bundle.

math.DG↗

arXiv2023

The Domino Problem of the Hyperbolic Plane for Regular Polygons

We provide a definitive classification of all finite sets of regular polygons that admit a tiling of the hyperbolic plane, thereby establishing the decidability of the Domino Problem for this class of prototiles. We show that admissibility is determined by a finite set of local and inductive combinatorial constraints. This classification further leads to the discovery of the first known examples of weakly aperiodic protosets consisting of regular polygons in $\mathbb{H}^2$.

math.CO↗

arXiv2023

On the Auerbach bases of $l^{n}_p$ spaces

In this paper, we study Auerbach basis of the Banach spaces $l^n_p$. We provide a complete classification of the spaces in terms of the cardinality of their bases. We also give a complete description of these bases for $l^3_p$ ($l^2_p$ is easy).

math.FA↗

arXiv2023

Some computations in string topology

In this paper, we discuss Hochschild chain models for some of the string topology operations. We use these models to simplify the proofs and computations of some of the results in string topology. Along the way we also make some new observations. We further discuss how nonnilpotent local level homology classes with respect to the Chas-Sullivan and the Goresky-Hingston product detect closed geodesics with optimal index growth rates.

math.DG↗

arXiv2020

Quasi-vertex-transitive Maps on the Plane

Quasi-vertex-transitive maps are the homogeneous maps on the plane with finitely many vertex orbits under the action of their automorphism groups. We show that there exist quasi-vertex-transitive maps of types $[p^3, 3]$ for $p \equiv 1$ (mod $6$), but there doesn't exist vertex-transitive map of such types. In particular, we determine the surface with the lowest possible genus that admit a polyhedral map of type $[5^3, 3]$.

math.GT↗