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Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).

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orbit space of $\mathbb{Z}_p$ action over complex projective space by permuting the homogene...

You can use $Z/5$ - Bredon cohomology of $CP^n$ with given action .Where the coefficient system is constant coeff. system.Then this Bredon cohomology gives the cohomology of the orbit space
Surojit Ghosh's user avatar