In the paper under review, the author starts from a spectral sequence defined by B. Gornik for Khovanov-Rozansky homology. The graded complex vector space H~i,jn(K) associated to Gornik's spectral sequence is supported in homological degree zero. The author shows that the quantum degrees of the nonzero H~0,jn(K) are determined only by an even integer sn(K). As a consequence sn(K) provides a lower bound for the smooth slice genus of K.
Review about "A note on Gornik's perturbation of Khovanov-Rozansky homology" by A. Lobb / Cristofori, Paola. - In: MATHEMATICAL REVIEWS. - ISSN 0025-5629. - ELETTRONICO. - MR2916277:(2012), pp. 0-0.
Review about "A note on Gornik's perturbation of Khovanov-Rozansky homology" by A. Lobb
CRISTOFORI, Paola
2012
Abstract
In the paper under review, the author starts from a spectral sequence defined by B. Gornik for Khovanov-Rozansky homology. The graded complex vector space H~i,jn(K) associated to Gornik's spectral sequence is supported in homological degree zero. The author shows that the quantum degrees of the nonzero H~0,jn(K) are determined only by an even integer sn(K). As a consequence sn(K) provides a lower bound for the smooth slice genus of K.
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