Topology Atlas | Conferences

Knots in Washington XXXVII
January 19-20, 2014
George Washington University
Washington, DC, USA

Mieczyslaw K. Dabkowski (UT Dallas), Valentina Harizanov (GWU), Jozef H. Przytycki (GWU and UMCP), Yongwu Rong (GWU), Radmila Sazdanovic (NCSU), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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Nonorientable genus of a knot in punctued CP2
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.