\BOOKMARK [1][-]{section.1}{Introduction}{} \BOOKMARK [2][-]{equation.1.1}{Notations}{section.1} \BOOKMARK [1][-]{section.2}{Existing invariants and results}{} \BOOKMARK [2][-]{subsection.2.1}{Invariants \340 la Merkurjev}{section.2} \BOOKMARK [3][-]{subsubsection.2.1.1}{Cycle modules}{subsection.2.1} \BOOKMARK [3][-]{subsubsection.2.1.2}{Gersten complex}{subsection.2.1} \BOOKMARK [3][-]{subsubsection.2.1.3}{Merkurjev's link}{subsection.2.1} \BOOKMARK [2][-]{subsection.2.2}{Platonov's examples}{section.2} \BOOKMARK [3][-]{subsubsection.2.2.1}{Cyclic algebras}{subsection.2.2} \BOOKMARK [3][-]{subsubsection.2.2.2}{Non-trivial SK1}{subsection.2.2} \BOOKMARK [3][-]{subsubsection.2.2.3}{Galois cohomology of Q p\(\(t1\)\)\(\(t2\)\)}{subsection.2.2} \BOOKMARK [2][-]{subsection.2.3}{Suslin's invariants}{section.2} \BOOKMARK [3][-]{subsubsection.2.3.1}{Suslin 1991}{subsection.2.3} \BOOKMARK [3][-]{subsubsection.2.3.2}{Biquaternion algebras}{subsection.2.3} \BOOKMARK [3][-]{subsubsection.2.3.3}{Suslin 2006}{subsection.2.3} \BOOKMARK [2][-]{subsection.2.4}{Kahn's invariants}{section.2} \BOOKMARK [3][-]{subsubsection.2.4.1}{Cyclicity of invariant group}{subsection.2.4} \BOOKMARK [3][-]{subsubsection.2.4.2}{Bounds on invariant group}{subsection.2.4} \BOOKMARK [3][-]{subsubsection.2.4.3}{Generalisation of Suslin's invariant}{subsection.2.4} \BOOKMARK [2][-]{subsection.2.5}{Generalising invariants}{section.2} \BOOKMARK [3][-]{subsubsection.2.5.1}{Logarithmic differentials}{subsection.2.5} \BOOKMARK [3][-]{subsubsection.2.5.2}{Lifts}{subsection.2.5} \BOOKMARK [1][-]{section.3}{Biquaternion algebras}{} \BOOKMARK [2][-]{subsection.3.1}{Definition}{section.3} \BOOKMARK [3][-]{subsubsection.3.1.1}{Involutions on Azumaya algebras}{subsection.3.1} \BOOKMARK [3][-]{subsubsection.3.1.2}{Witt groups}{subsection.3.1} \BOOKMARK [3][-]{subsubsection.3.1.3}{Definition}{subsection.3.1} \BOOKMARK [2][-]{subsection.3.2}{Comparison, moderate case}{section.3} \BOOKMARK [2][-]{subsection.3.3}{Comparison, wild case}{section.3} \BOOKMARK [3][-]{subsubsection.3.3.1}{Lifting algebras with involution}{subsection.3.3} \BOOKMARK [3][-]{subsubsection.3.3.2}{Preparing the ingredients}{subsection.3.3} \BOOKMARK [3][-]{subsubsection.3.3.3}{Cooking up the result}{subsection.3.3} \BOOKMARK [2][-]{subsection.3.4}{Non-triviality of the invariant}{section.3} \BOOKMARK [1][-]{section.4}{Comparing to Kahn's invariant}{} \BOOKMARK [2][-]{subsection.4.1}{Moderate case}{section.4} \BOOKMARK [3][-]{subsubsection.4.1.1}{Ways of looking}{subsection.4.1} \BOOKMARK [3][-]{subsubsection.4.1.2}{Determining factors}{subsection.4.1} \BOOKMARK [3][-]{subsubsection.4.1.3}{Non-triviality of Kahn's invariants}{subsection.4.1} \BOOKMARK [2][-]{subsection.4.2}{Wild case}{section.4} \BOOKMARK [2][-]{subsection.4.3}{Formula on the centre}{section.4} \BOOKMARK [3][-]{subsubsection.4.3.1}{General result}{subsection.4.3} \BOOKMARK [3][-]{subsubsection.4.3.2}{Non-triviality of factor}{subsection.4.3} \BOOKMARK [1][-]{lemma.4.13}{Bibliography}{}