175 research outputs found
History of bank robberies
No full textDouglas College and the New Westminster Museum collaborated to host the Tick-Talk: Crime and Consequences Student Conference, which featured criminology students' presentations on a variety of crime, justice, and social issues. Adopting a fast-paced presentation format, students raised key issues and challenges, described personal experiences, and disseminated unique ideas in a public forum. Presentation topics included the right to legal representation, the over representation of Indigenous peoples in Canada’s criminal justice system, youth justice policy, and connections between mental health and criminal justice. The conference also included several discussion sessions that generated valuable dialogue among students, academics, practitioners, and members of the public. --- Katherine Mrowka presented on the history of bank robberies, specifically the prevalence of armed bank robberies in New Westminster in the 1970s. Mrowka compared this criminal activity to today's steep decline in bank robberies and examined modern banking security.Not peer reviewe
Khovanov homology is an unknot-detector
No full textWe prove that a knot is the unknot if and only if its reduced Khovanov cohomology has rank 1. The proof has two steps. We show first that there is a spectral sequence beginning with the reduced Khovanov cohomology and abutting to a knot homology defined using singular instantons. We then show that the latter homology is isomorphic to the instanton Floer homology of the sutured knot complement: an invariant that is already known to detect the unknot
Spacesof continuous functions defined on Mrowka spaces
No full textWe prove that for a maximal almost disjoint family A on omega, the space C-p(Psi (A), 2(omega)) of continuous Cantor-valued functions with the pointwise convergence topology defined on the Mrowka space Psi (A) is not normal. Using CH we construct a maximal almost disjoint family A for which the space C-p( Psi (A), 2) of continuous {0, 1}-valued functions defined on Psi (A) is Lindelof. These theorems improve some results due to Dow and Simon in [Spaces of continuous functions over a Psi-space, Preprint]. We also prove that this space C-p (Psi (A), 2) = X is a Michael spac
Instanton Floer homology and the Alexander polynomial
No full textThe instanton Floer homology of a knot in the three-sphere is a vector space with a canonical mod 2 grading. It carries a distinguished endomorphism of even degree, arising from the 2–dimensional homology class represented by a Seifert surface. The Floer homology decomposes as a direct sum of the generalized eigenspaces of this endomorphism. We show that the Euler characteristics of these generalized eigenspaces are the coefficients of the Alexander polynomial of the knot. Among other applications, we deduce that instanton homology detects fibered knots.National Science Foundation (U.S.) (grant DMS-0206485)National Science Foundation (U.S.) (grant DMS-0244663)National Science Foundation (U.S.) (grant DMS-0805841
Seiberg-witten equations, end-periodic dirac operators, and a lift of Rohlin's invariant
No full textAuthor Manuscript: 4 Apr 2011We introduce a gauge-theoretic integer valued lift of the Rohlin
invariant of a smooth 4-manifold X with the homology of S[superscript 1]×S[superscript 3].
The invariant has two terms: one is a count of solutions to the
Seiberg–Witten equations on X, and the other is essentially the
index of the Dirac operator on a non-compact manifold with end
modeled on the infinite cyclic cover of X. Each term is metric
(and perturbation) dependent, and we show that these dependencies
cancel as the metric and perturbation vary in a generic
1-parameter family
Exact Triangles for SO(3) Instanton Homology of Webs
No full textThe SO(3) instanton homology recently introduced by the authors associates a finite-dimensional vector space over the field of two elements to every embedded trivalent graph (or "web"). The present paper establishes a skein exact triangle for this instanton homology, as well as a realization of the octahedral axiom. From the octahedral diagram, one can derive equivalent reformulations of the authors' conjecture that, for planar webs, the rank of the instanton homology is equal to the number of Tait colorings.National Science Foundation (U.S.) (Grant DMS-0805841)National Science Foundation (U.S.) (Grant DMS-1406348
Gauge theory and Rasmussen's invariant
No full textUsing a version of instanton homology, an integer invariant s[superscript ♯](K) is defined for knots K in S[superscript 3]. This invariant is shown to be equal to Rasmussen's s-invariant. While Rasmussen's invariant provides a lower bound for 2 g(Σ) for any surface Σ in B[superscript 4] with boundary K, it is shown in this paper that s[superscript ♯](K) (and therefore s(K)) similarly bounds the genus of such a surface Σ in any homotopy 4-ball.National Science Foundation (U.S.) (Grant DMS-0805841
Knot homology groups from instantons
No full textFor each partial flag manifold of SU(N), we define a Floer homology theory for knots in 3-manifolds, using instantons with codimension-2 singularities. In the case of SU(2), the resulting Floer homology group for classical knots appears to be related to Khovanov homology.National Science Foundation (U.S.) (Grant DMS-0206485)National Science Foundation (U.S.) (Grant DMS-0244663)National Science Foundation (U.S.) (Grant DMS-0805841
Filtrations on instanton homology
No full textIn earlier work of the authors, the Khovanov complex of a knot or link appeared as the first page in a spectral sequence abutting to the instanton homology. The quantum and (co)homological gradings on Khovanov homology do not survive as gradings, but we show that they survive as filtrations.National Science Foundation (U.S.) (Grant DMS-0805841
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