Abstract: We shall begin with the homotopy invariance property of K-theory.After reviewing monoids and monoid algebras, we present some results which aremonoid version of the homotopy invariance property in K-theory. This answers a question ofGubeladze. Next, we will discuss the monoid version of Weibel's vanishing conjectureand some results in this direction. Finally, we will talk about the homology stability for groups.Here we present a result which improves homology stability for symplectic groups.If the time permits, some application of the homology stability will be given to the hermitian K-theory.
sms seminar hall
Dr. Pervez Sarwar
Algebraic K-theory and homology stability