Advisors
Now showing items 18 of 8

2fold structures and homotopy theory
(Bilkent University, 202301)It is wellknown that correspondences between categories, also known as profunctors, serve in classifying functors. More precisely, every functor F : X → A straightens into a lax mapping χF : A → Catprof from A into a ... 
Cobordism calculations with Adams and James spectral sequences
(Bilkent University, 2010)Let ξn : Z/p → U(n) be an ndimensional faithful complex representation of Z/p and in : U(n)→O(2n) be inclusion for n ≥ 1. Then the compositions in ◦ ξn and jn ◦ in ◦ ξn induce fibrations on BZ/p where jn : O(2n) → O(2n ... 
Concrete sheaves and continuous spaces
(Bilkent University, 2015)In algebraic topology and differential geometry, most categories lack some good ”convenient” properties like being cartesian closed, having pullbacks, pushouts, limits, colimits... We will introduce the notion of continuous ... 
A conjecture on squarezero upper triangular matrices and Carlsson's rank conjecture
(Bilkent University, 201809)A wellknown conjecture states that if an elementary abelian pgroup acts freely on a product of spheres, then the rank of the group is at most the number of spheres in the product. Carlsson gives an algebraic version ... 
Finite psubgroups of Sp(n)
(Bilkent University, 202109)Hikari [1] classiﬁes all ﬁnite psubgroups of simple algebras, and Banieqbal [2] classiﬁes the ﬁnite subgroups of 2×2 matrices over a division algebra of characteristic zero. In this thesis, we give a new proof for the ... 
Free actions on CWcomplexes and varieties of square zero matrices
(Bilkent University, 2011)Gunnar Carlsson stated a conjecture which gives a lower bound on the rank of a differential graded module over a polynomial ring with coefficients in algebraically closed field k when it has a finite dimensional homology ... 
The geometry of sheaves on sites
(Bilkent University, 202101)In this work, we study doing geometry on sheaves on sites. Categories of our sites consist of objects that are building blocks for a given geometry. Generalized spaces then will be sheaves on these sort of sites. Next we ... 
Monoid actions, their categorification and applications
(Bilkent University, 201612)We study actions of monoids and monoidal categories, and their relations with (co)homology theories. We start by discussing actions of monoids via biactions. We show that there is a welldefined functorial reverse action ...