10 papers
Prehomogeneous geometries vs. bundles with connections
Ercüment Ortaçgil
The below discussion is in three sections A, B, C, each section in two parts I, II, I representing the standpoint of bundles with connections and II representing the standpoint of…
Klein geometries of high order
Ercüment H. Ortaçgil
Using irreducible representations of semi simple Lie algebras, we construct Klein geometries of arbitrarily high order.
On Hadwiger-Alesker finiteness theorem
Ercüment Ortaçgil
We study the Hadwiger-Alesker finiteness theorem from the standpoint of Lie theory and announce a generalization.
The structure constants of geometric structures on a local Lie group
Ercüment H. Ortaçgil
We define the structure constants of almost complex, almost symplectic and Riemannian structures on a local Lie group
On a simple proof the Poincare Conjecture
Ercüment Ortaçgil
We outline a simple proof of PC without surgeries using the homogeneous flow introduced in [O].
The homogeneous flow of a parallelizable manifold
Ercüment Ortaçgil
Motivated by the Hamilton's Ricci flow, we define the homogeneous flow of a parallelizable manifold and show the long time existence and uniqueness of its solutions on $[0,\infty).…
Characteristic classes as obstructions to local homogeneity
Ercüment Ortaçgil
This note is an extended version of my presentation at the "Focused Research Workshop on Exterior Di§erential Systems and Lie Theory" held at the Fields Institute in Toronto, Decem…
Horizontal cohomology of a local Lie group
Ercüment Ortaçgil
We define and study the invariant linear and nonlinear horizontal double complexes of a local Lie group.
Tensor calculus and deformation theory on on a local Lie group
Ercüment Ortaçgil
Historically tensor calculus emerged in an attempt to formalize Rie- mann's ideas. We show that tensor calculus can be based also on Lie's idea of a transformation group and this a…
The heritage of S.Lie and F.Klein: Geometry via transformation groups
Ercüment Ortaçgil
We outline a framework which generalizes Felix Klein's Erlanger Programm which he announced in 1872 after exchanging ideas with Sophus Lie.