Odd Khovanov homology, mutation, and branched double covers

Jonathan Bloom

Knots in Washington XXIX; 30 years of quandles, 10 years of Khovanov homology
December 4-6, 2009
George Washington University
Washington, DC, USA

Organizers
Jozef H. Przytycki (GWU), Yongwu Rong (GWU, NSF), Radmila Sazdanovic (GWU), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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Odd Khovanov homology, mutation, and branched double covers
by
Jonathan Bloom
Columbia University

We describe a thriftier construction of odd Khovanov homology, motivated by branched double covers. As a simple application, we prove that odd Khovanov homology is mutation invariant, and therefore that mod 2 Khovanov homology is mutation invariant. As a second application, we outline an extensive connection to monopole Floer homology.

Paper reference: arXiv:0903.3746, arXiv:0909.0816

Date received: October 6, 2009