GRID DIAGRAMS AND THE OZSVATH-SZABO TAU-INVARIANT

作者：Sarkar Sucharit^*

来源：Mathematical Research Letters, 2011, 18(6): 1239-1257.

• Knot cobordism
• Ozsvath-Szabo invariant
• Milnor conjecture
• Grid diagram

We use grid diagrams to investigate the Ozsvath-Szabo concordance invariant tau, and to prove that vertical bar tau(K-1) - tau(K-2)vertical bar <= g, whenever there is a genus g knot cobordism joining K-1 to K-2. This leads to an entirely grid diagram-based proof of Kronheimer-Mrowka's theorem, formerly known as the Milnor conjecture.

• 出版日期2011