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Nonorientable genus of a knot in punctued CP2
by
Kouki Sato
Tokyo Gakugei University
Coauthors: Motoo Tange (University of Tsukuba)
Let K be a knot in ∂(CP2 - Int B4) and F ⊂ CP2 - Int B4 a smoothly embedded nonorientable surface with boundary K. We prove that if F represents zero in H2( CP2 - Int B4, ∂( CP2 - Int B4); Z2), then β1(F) ≥ - σ(K)/2 + d(S31(K)) - 1, where d(S31(K)) is the Heegaard Floer d-invariant of the integer homology sphere given by 1 surgery on K. In particular, if K is #n 942, 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 # cbid-08.