arXiv subjects
Publications and source records attributed to Mehmet Kirdar.
In this note, we will consider two classical volume problems related to elliptic integrals. The first problem has a neat formula by means of elliptic integrals. We remade it with details. In the second problem, we found a messy formula. On the other hand, it seems to be useful to find a good approximation for the volume.
We describe the first stem of the stable homotopy groups of spheres by using some Puppe sequences, Thom complexes, K-Theory and Adams operations following the ideas of J. Frank Adams. We also touch upon the second and the third stems in this perspective. Neither spectral squences nor Steenrod operations are used.
We describe $K(BS_4)$ and make a connection of the order of the bundle induced from the standart representation over the four dimensional skeleton of $BS_4$ with the stable homotopy group $π_3^s=Z_{24}$ explaining the reasons of this connection by pulling this bundle over lens spaces.
We describe the J-Groups of lens spaces modulo odd prime powers via relations and rational representations.
We describe the K-ring of the classifying space of the dihedral group in terms of generators and the minimal set of relations by emphasising the connection with the polynomials arising in the KO-rings of lens spaces and demonstrating the generators of the filtrations of the Atiyah-Hirzebruch Spectral Squence.
We describe the K-ring of the classifying space of the generalized quaternion group in terms of generators and the minimal set of relations. We also compute the order of the main generator in the truncated rings.