arXiv subjects

Subhankar Sau

Publications and source records attributed to Subhankar Sau.

7 recordsLinked to original sources

arXiv2026

On Generalized Milnor Manifolds and Their Topological Complexity

We introduce generalized Milnor manifolds (GMM), extending the classical Milnor manifolds over $\mathbb{R}$, $\mathbb{C}$, and $\mathbb{H}$. We compute their integral cohomology algebras in the complex and quaternionic cases and their mod-$2$ cohomology algebras in the real case. We compare GMM with partial flag manifolds, investigate when they are homotopy equivalent, and obtain a necessary and sufficient condition in the complex and quaternionic cases. We further prove that complex GMM are K\"ahler manifolds. As an application, we determine their higher topological complexities, obtaining exact values in the complex and quaternionic cases and bounds in the real case. Along the way, for a fibre bundle satisfying the Leray--Hirsch hypothesis, we establish a lower bound for the zero-divisor cup-length of the total space in terms of base and fibre.

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arXiv2025

Parametrized Topological Complexity for a Multi-Robot System with Variable Tasks

We study a generalized motion planning problem involving multiple autonomous robots navigating in a $d$-dimensional Euclidean space in the presence of a set of obstacles whose positions are unknown a priori. Each robot is required to visit sequentially a prescribed set of target states, with the number of targets varying between robots. This heterogeneous setting generalizes the framework considered in the prior works on sequential parametrized topological complexity by Farber and the second author of this article. To determine the topological complexity of our problem, we formulate it mathematically by constructing an appropriate fibration. Our main contribution is the determination of this invariant in the generalized setting, which captures the minimal algorithmic instability required for designing collision-free motion planning algorithms under parameter-dependent constraints. We provide a detailed analysis for both odd and even-dimensional ambient spaces, including the essential cohomological computations and explicit constructions of corresponding motion planning algorithms.

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arXiv2024

$SU(2)$-bundles over highly connected $8$-manifolds

In this paper, we analyze the possible homotopy types of the total space of a principal $SU(2)$-bundle over a $3$-connected $8$-dimensional Poincaré duality complex. Along the way, we also classify the $3$-connected $11$-dimensional complexes $E$ formed from a wedge of $S^4$ and $S^7$ by attaching a $11$-cell.

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arXiv2023

Blowdown, $k$-wedge and evenness of quasitoric orbifolds

In this paper, we introduce polytopal $k$-wedge construction and blowdown of a simple polytope and inspect the effect on the retraction sequence of a simple polytope due to $k$-wedge construction and blowdown. In relation to this construction, we introduce the $k$-wedge and blowdown of a quasitoric orbifold. We compare the torsions in the integral cohomologies of $k$-wedges and blowdowns of a quasitoric orbifold with the original one. These two constructions provide infinitely many integrally equivariantly formal quasitoric orbifolds from a given one.

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arXiv2023

Various Topological Complexities of Small Covers and Real Bott Manifolds

In this paper, we compute the LS-category and equivariant LS-category of a small cover and its real moment angle manifold. We calculate a tight lower bound for the topological complexity of many small covers over a product of simplices. Then we compute symmetric topological complexity of several small covers over a product of simplices. We calculate the LS one-category of real Bott manifolds and infinitely many small covers.

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arXiv2022

On cohomology of quasitoric manifolds over a vertex cut of a finite product of simplices

In this paper, we classify the characteristic matrices associated to quasitoric manifolds over a vertex cut of a finite product of simplices. We discuss the integral cohomology rings of these quasitoric manifolds with possibly minimal generators and show several relations among the product of these generators. We classify integral cohomology rings (up to isomorphism as graded rings) of the quasitoric manifolds over the vertex cut of a finite product of simplices.

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arXiv2022

Resolution of singularities of toric orbifolds and equivariant cobordism of contact toric manifolds

Toric orbifolds are a generalization of simplicial projective toric varieties. In this paper, we show that there is a resolution of singularities of a toric orbifold. In a different category, the class of quasi-contact toric manifolds contains the class of good contact toric manifolds. We prove that a quasi-contact toric manifold is equivariantly a boundary. Moreover, we conclude that good contact toric manifolds and generalized lens spaces are equivariantly boundaries.

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