All Outputs (24)

A note on Gornik's perturbation of Khovanov-Rozansky homology (2012)
Journal Article
Lobb, A. (2012). A note on Gornik's perturbation of Khovanov-Rozansky homology. Algebraic & geometric topology, 12(1), 293-305. https://doi.org/10.2140/agt.2012.12.293

We show that the information contained in the associated graded vector space to Gornik’s version of Khovanov–Rozansky knot homology is equivalent to a single even integer sn(K). Furthermore we show that sn is a homomorphism from the smooth knot conco... Read More about A note on Gornik's perturbation of Khovanov-Rozansky homology.

Computable bounds for Rasmussen's concordance invariant (2011)
Journal Article
Lobb, A. (2011). Computable bounds for Rasmussen's concordance invariant. Compositio Mathematica, 147(2), 661-668. https://doi.org/10.1112/s0010437x10005117

Given a diagram D of a knot K, we give easily computable bounds for Rasmussen’s concordance invariant s(K). The bounds are not independent of the diagram D chosen, but we show that for diagrams satisfying a given condition the bounds are tight. As a... Read More about Computable bounds for Rasmussen's concordance invariant.

On Casson-type instanton moduli spaces over negative definite 4-manifolds (2010)
Journal Article
Lobb, A., & Zentner, R. (2010). On Casson-type instanton moduli spaces over negative definite 4-manifolds. The Quarterly Journal of Mathematics, 62(2), 433-450. https://doi.org/10.1093/qmath/hap042

Recently Andrei Teleman considered instanton moduli spaces over negative definite 4-manifolds X with b2(X) ≥ 1. If b2(X) is divisible by four and b1(X) = 1 a gauge-theoretic invariant can be defined; it is a count of flat connections modulo the gauge... Read More about On Casson-type instanton moduli spaces over negative definite 4-manifolds.

A slice genus lower bound from sl(n) Khovanov-Rozansky homology (2009)
Journal Article
Lobb, A. (2009). A slice genus lower bound from sl(n) Khovanov-Rozansky homology. Advances in Mathematics, 222(4), 1220-1276. https://doi.org/10.1016/j.aim.2009.06.001

We show that a generic perturbation of the doubly-graded Khovanov–Rozansky knot homology gives rise to a lower-bound on the slice genus of a knot. We prove a theorem about obtainable presentations of surfaces embedded in 4-space, which we use to simp... Read More about A slice genus lower bound from sl(n) Khovanov-Rozansky homology.