
Organizers 
Nonorientable genus of a knot in punctued CP^{2}
by
Kouki Sato
Tokyo Gakugei University
Coauthors: Motoo Tange (University of Tsukuba)
Let K be a knot in ∂(CP^{2}  Int B^{4}) and F ⊂ CP^{2}  Int B^{4} a smoothly embedded nonorientable surface with boundary K. We prove that if F represents zero in H_{2}( CP^{2}  Int B^{4}, ∂( CP^{2}  Int B^{4}); Z_{2}), then β_{1}(F) ≥  σ(K)/2 + d(S^{3}_{1}(K))  1, where d(S^{3}_{1}(K)) is the Heegaard Floer dinvariant of the integer homology sphere given by 1 surgery on K. In particular, if K is #_{n} 9_{42}, then the minimal first Betti number of such surfaces is equal to n  1.
Date received: November 26, 2013
Copyright © 2013 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbid08.