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Homological monotonicity for configuration spaces of manifolds
Muhammad Yameen
Consider the configuration spaces of manifolds. An influential theorem of McDuff, Segal and Church shows that the (co)homology of the unordered configuration space is independent o…
Arithmeticity for integral cohomological dimension of configuration spaces of manifolds
Muhammad Yameen
Consider the configuration spaces of manifolds. We give a precise formula for the integral cohomological dimension (the degree of top non-trivial integral cohomology group) of unor…
On the limiting extremal vanishing for configuration spaces
Muhammad Yameen
We study the limiting behavior of extremal cohomology groups of -points configuration spaces of complex projective spaces of complex dimension In the previous work, w…
A remark on extremal stability of configuration spaces
Muhammad Yameen
We explicitly study the extremal stability of configuration spaces of complex projective spaces of any dimension, and show that the homology groups are vanish in extremal stable ra…
Strong stability and shifted stability for the cohomology of configuration spaces
Barbu Berceanu, Muhammad Yameen
Homological stability for unordered configuration spaces of connected manifolds was discovered by Th. Church and extended by O. Randal-Williams and B. Knudsen: $H_i(C_k(M);\mathbb{…