arXiv subjects

Sagnik Biswas

Publications and source records attributed to Sagnik Biswas.

3 recordsLinked to original sources

arXiv2026

Smooth manifolds homotopy equivalent to products of spheres

We classify, up to almost diffeomorphism, the smooth closed oriented manifolds homotopy equivalent to each of the sphere products $S^{4k-1}\times S^{4k}$, $S^{4k}\times S^{4k}$, and $S^{4k}\times S^{4k+1}$. In each case we realize the image of the normal-invariant map in the smooth surgery exact sequence by explicit families of manifolds: sphere bundles over $S^{4k}$; pinch maps and Milnor plumbings of disk bundles; and Novikov sphere bundles together with connected sums of homotopy spheres.

math.AT↗

arXiv2026

Rigidity of self-maps of $V_{n,2}$ and manifolds tangentially homotopy equivalent to $V_{n,2} \times S^k$

We study two problems concerning the Stiefel manifolds $V_{n,2}$ and their products with spheres. First, we address a rigidity problem: we determine, for most values of~$n$, all self-maps of $V_{n,2}$ that are homotopic to an almost diffeomorphism. Second, we classify smooth closed manifolds tangentially homotopy equivalent to $V_{n,2} \times S^k$ up to almost diffeomorphism, for $k = 3, 5$ or $7 \leq k, k \neq 2^i - 2 \ \text{and} \ Dim(V_{n,2} \times S^k) \neq 2^i - 2$. Our method is to find explicit inverses in the structure set via normal invariants of specific tangential homotopy equivalences. In favourable cases -- notably $V_{12,2} \times S^3$, $V_{16,2} \times S^3$, $V_{10,2} \times S^5$ -- the classification is complete: every such manifold is almost diffeomorphic to $V_{n,2} \mathbin{\#} \Sigma \times S^k$ for some exotic sphere $\Sigma$. In the general case, we identify inverses for a large subgroup of $\operatorname{Im}(\eta)$ and provide a reasonable direction for the remainder.

math.AT↗

arXiv2008

Design of a Fractional Order PID Controller Using Particle Swarm Optimization Technique

Particle Swarm Optimization technique offers optimal or suboptimal solution to multidimensional rough objective functions. In this paper, this optimization technique is used for designing fractional order PID controllers that give better performance than their integer order counterparts. Controller synthesis is based on required peak overshoot and rise time specifications. The characteristic equation is minimized to obtain an optimum set of controller parameters. Results show that this design method can effectively tune the parameters of the fractional order controller.

cs.OH↗