7 papers · 1 filter
Equivariant persistence topological complexity
Navnath Daundkar, Ankur Sarkar, Bittu Singh
We introduce equivariant persistent analogues of Lusternik-Schnirelmann category, topological complexity, cup length, and zero-divisors cup length for persistent spaces with group…
On the Sequential topological complexity of directed (parametrized) motion planning algorithms
Navnath Daundkar, Abhishek Sarkar, Ankur Sarkar
We introduce sequential analogues of directed (parametrized) topological complexity, in the context of motion planning problems requiring a system to traverse a prescribed sequence…
A Precise Treatment of Soft Quotient Topology and Soft Covering Maps
Souvik Mandal, Ankur Sarkar
We develop a foundational theory of soft quotient topology, providing a systematic approach to quotient constructions in soft topological spaces. We establish the universal propert…
Relative Smooth Surgery Structure Sets of Thickenings of the Cayley Projective Plane and Applications
Souvik Mandal, Ankur Sarkar
We compute the relative smooth surgery structure sets of the thickenings of the Cayley projective plane for every …
Countable Fan Tightness and Selection Games in Group-Valued Function Spaces
Souvik Mandal, Ankur Sarkar
Game-theoretic characterizations of selection principles provide a powerful framework for analyzing covering properties through strategic interactions. For a Tychonoff space an…
Prime Density, Kolmogorov Quotients and Homeomorphisms between Macías Spaces of Integral Domains
Souvik Mandal, Ankur Sarkar
For an integral domain that is not a field, the Macías space is the set endowed with the topology generated by the subsets $σ_k^0=\{x\in R^0:\langl…
On sequential versions of various parametrized invariants
Navnath Daundkar, Abhishek Sarkar, Ankur Sarkar
In this paper, we introduce and study sequential versions of several fibrewise homotopy invariants, including parametrized topological complexity, parametrized (subspace) homotopic…