Sažetak KiDM 20100513

Izvor: KiWi

Abstract: The homology of the group SL3(Z) was determined by Soule. The notion of group homology can be defined from the action of a group acting fixed point free on a space X. For the group SL3(Z) and PSL4(Z) it is not easy to find such space, but if one make such groups act on the space of quadratic form, then one gets an action whose stabilizers are finite. We can then apply perturbation techniques and compute some homology groups. In particular we found the groups H_n(PSL4(Z),Z) for n<=5 and we computed explicitly the 5-part of those groups.