Ramesh Kasilingam

activity

20152026

most citedFarrell-Jones spheres and inertia groups of complex projective spaces

5 citations · 11 across the 10 of their papers we have counts for

collaborators

14 papers

math.AT2026

Diffeomorphism Classification of Smooth Structures and Tangential Homotopy Types of $C P^{m}$ for $5 \leq m \leq 8$

Ramesh Kasilingam

This paper provides a diffeomorphism classification of smooth manifolds homeomorphic to the complex projective space $C P^{m}$ for $m \in {5, 6, 7, 8}$ . The classification…

math.AT2025

Enumerating Smooth Structures on $C P^{3} \times S^{k}$

Samik Basu, Ramesh Kasilingam, Ankur Sarkar

In this paper, we compute the concordance inertia group of the product $M \times S^{k}$ , where $M$ is a simply connected, closed, smooth 6-manifold, for $1 \leq k \leq 10$ ,…

math.CO2024

On the Classification of Planar-Rips complexes and their corresponding unit disk graphs

Vinay Sipani, Ramesh Kasilingam

Given a metric space $(X, d)$ , the Vietoris-Rips complex of $X$ at a scale of $r > 0$ is a simplicial complex whose simplices are all those finite subsets of $X$ with diameter less t…

math.AT2024

Smooth Structures on $M \times S^{k}$

Samik Basu, Ramesh Kasilingam, Ankur Sarkar

This paper explores various differentiable structures on the product manifold $M \times S^{k}$ , where $M$ is either a 4-dimensional closed, oriented, smooth manifold or a si…

math.AT2023

Smooth structures on PL-manifolds of dimensions between 8 and 10

Samik Basu, Ramesh Kasilingam, Priyanka Magar-Sawant

In this paper, we identify the concordance classes of smooth structures on $P L$ -manifolds of dimension between $8$ and $10$ in terms of the cohomology and Steenrod operations. This…

math.GT2017★ 3 cited

Inertia Groups and Smooth Structures on Quaternionic Projective Spaces

Samik Basu, Ramesh Kasilingam

This paper deals with certain results on the number of smooth structures on quaternionic projective spaces, obtained through the computation of inertia group and its analogues, whi…

math.GT2015

Homotopy Inertia Groups and Tangential Structures

Ramesh Kasilingam

We show that if $M$ and $N$ have the same homotopy type of simply connected closed smooth $m$ -manifolds such that the integral and mod- $2$ cohomologies of $M$ vanish in odd degrees…

math.GT2015

Topological Rigidity Problems

Ramesh Kasilingam

We survey the recent results and current issues on the topological rigidity problem for closed aspherical manifolds, i.e., connected closed manifolds whose universal coverings are…

math.GT2015

Smooth and PL-Rigidity Problems on Locally Symmetric Spaces

Ramesh Kasilingam

This is a survey on known results and open problems about Smooth and PL-Rigidity Problem for negatively curved locally symmetric spaces. We also review some developments about stud…

math.GT2015

The classification of smooth structures on a homotopy complex projective space

Ramesh Kasilingam

We classify, up to diffeomorphism, all closed smooth manifolds homeomorphic to the complex projective $n$ -space $C P^{n}$ , where $n = 3$ and $4$ . Let $M^{2 n}$ be a clo…

math.GT2015★ 1 cited

Inertia groups and smooth structures of $(n - 1)$ -connected $2 n$ -manifolds

Ramesh Kasilingam

Let $M^{2 n}$ denote a closed $(n - 1)$ -connected smoothable topological $2 n$ -manifold. We show that the group $C (M^{2 n})$ of concordance classes of smoothings of $M^{2 n}$ i…

math.GT2015★ 5 cited

Farrell-Jones spheres and inertia groups of complex projective spaces

Ramesh Kasilingam

We introduce and study a new class of homotopy spheres called Farrell-Jones spheres. Using Farrell-Jones sphere we construct examples of closed negatively curved manifolds $M^{2 n}$ …

math.AT2015★ 2 cited

Inertia groups of high dimensional complex projective spaces

Samik Basu, Ramesh Kasilingam

For a complex projective space the inertia group, the homotopy inertia group and the concordance inertia group are isomorphic. In complex dimension 4n+1, these groups are related t…

math.GT2015

Smooth Structures on a Fake Real Projective Space

Ramesh Kasilingam

We show that the group of smooth homotopy $7$ -spheres acts freely on the set of smooth manifold structures on a topological manifold $M$ which is homotopy equivalent to the real pr…

Diffeomorphism Classification of Smooth Structures and Tangential Homotopy Types of CPm for 5≤m≤8

Enumerating Smooth Structures on CP3×Sk

On the Classification of Planar-Rips complexes and their corresponding unit disk graphs

Smooth Structures on M×Sk

Smooth structures on PL-manifolds of dimensions between 8 and 10

Inertia Groups and Smooth Structures on Quaternionic Projective Spaces

Homotopy Inertia Groups and Tangential Structures

Topological Rigidity Problems

Smooth and PL-Rigidity Problems on Locally Symmetric Spaces

The classification of smooth structures on a homotopy complex projective space

Inertia groups and smooth structures of (n−1)-connected 2n-manifolds

Farrell-Jones spheres and inertia groups of complex projective spaces

Inertia groups of high dimensional complex projective spaces

Smooth Structures on a Fake Real Projective Space

Diffeomorphism Classification of Smooth Structures and Tangential Homotopy Types of $C P^{m}$ for $5 \leq m \leq 8$

Enumerating Smooth Structures on $C P^{3} \times S^{k}$

Smooth Structures on $M \times S^{k}$

Inertia groups and smooth structures of $(n - 1)$ -connected $2 n$ -manifolds