Chennai Mathematical Institute


Topic: CMI Mathematics Seminar
Date: Thursday, March 4, 2021.
Time: 3:30 PM.
Tidiness of planar polygonal spaces

Shuchita Goyal
Chennai Mathematical Institute.


Configuration spaces of mechanical linkages are quite important and have engineering applications. These spaces gave rise to a new mathematical subject - Topological Robotics; and have extensively been studied by Farber, Panina and others. A mechanical linkage is a mechanism built from stiff bars (called rigid links) connected at freely rotating joints. The configuration space of such a linkage is the set of all its possible states.

We would be focusing on the closed linkages with $n$ rigid links (this gives an $n$-length vector whose $i$-th coordinate corresponds to the length of $i$-th rigid link) that are allowed to rotate in a plane, giving rise to a \it{planar} polygonal space. This talk would see some analysis of these spaces from a topological point of view.

For a topological space, there are two invariants, namely coindex and index, such that coindex is never more than the index of the space. The space is said to be tidy if these two invariants coincide with each other. We would see which planar polygonal spaces (with specific length vectors) are tidy in this talk. This is joint work with Navnath Daundekar, Priyavrat Deshpande, Anurag Singh.