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Equivariant Cohomology of Configuration Spaces mod 2: The State of the Art
Pavle V. M. Blagojević, Frederick R. Cohen, Michael C. Crabb +2
The equivariant cohomology of the classical configuration space has been been of great interest and has been studied intensively starting with the classical pap…
Polynomial partitioning for several sets of varieties
Pavle V. M. Blagojević, Aleksandra S. Dimitrijević Blagojević, Günter M. Ziegler
We give a new, systematic proof for a recent result of Larry Guth and thus also extend the result to a setting with several families of varieties: For any integer and any…
Hyperplane mass partitions via relative equivariant obstruction theory
Pavle V. M. Blagojević, Florian Frick, Albert Haase +1
The Grünbaum-Hadwiger-Ramos hyperplane mass partition problem was introduced by Grünbaum (1960) in a special case and in general form by Ramos (1996). It asks for the "admissible"…
Equivariant Topology of Configuration Spaces
Pavle V. M. Blagojević, Wolfgang Lück, Günter M. Ziegler
We study the Fadell-Husseini index of the configuration space F(R^d,n) with respect to different subgroups of the symmetric group S_n. For p prime and d>0, we completely determine…
Convex Equipartitions via Equivariant Obstruction Theory
Pavle V. M. Blagojević, Günter M. Ziegler
We describe a regular cell complex model for the configuration space F(\R^d,n). Based on this, we use Equivariant Obstruction Theory to prove the prime power case of the conjecture…
Dwyer-Kan homotopy theory of enriched categories
Fernando Muro
We construct a model structure on the category of small categories enriched over a combinatorial closed symmetric monoidal model category satisfying the monoid axiom. Weak equivale…
Optimal bounds for a colorful Tverberg--Vrecica type problem
Pavle Blagojevic, Benjamin Matschke, Gunter Ziegler
We prove the following optimal colorful Tverberg-Vrecica type transversal theorem: For prime r and for any k+1 colored collections of points C^l of size |C^l|=(r-1)(d-k+1)+1 in R^d…
Tetrahedra on deformed spheres and integral group cohomology
Pavle V. M. Blagojevic, Günter M. Ziegler
We show that for every injective continuous map f: S^2 --> R^3 there are four distinct points in the image of f such that the convex hull is a tetrahedron with the property that tw…