Using an obstruction based on Donaldson's theorem on the intersection forms of definite 4-manifolds, we determine which connected sums of lens spaces smoothly embed in S 4 . We also find constraints on the Seifert invariants of Seifert 3-manifolds which embed in S 4 when either the base orbifold is non-orientable or the first Betti number is odd. In addition, we construct some new embeddings and use these, along with the d and μ invariants, to examine the question of when the double branched cover of a 3 or 4 strand pretzel link embeds.

We define a notion of concordance based on Euler characteristic, and show that it gives rise to a concordance group L of links in S 3 , which has the concordance group of knots as a direct summand with infinitely generated complement. We consider variants of this using oriented and unoriented surfaces as well as smooth and locally flat embeddings.57M25, 57M27, 57N70

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Abstract. From Furuta's 10 8 theorem, we derive a smooth slicing obstruction for knots in S 3 using a spin 4-manifold whose boundary is 0-surgery on a knot. We show that this obstruction is able to detect torsion elements in the smooth concordance group and find topologically slice knots which are not smoothly slice.

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This case study examines the changes that were made to workshops for first year mathematics students when moving from in-person to online in the 2020/21 academic year. In the workshops, students tackle unfamiliar problems in small groups, with a focus on group work and mathematical communication skills. Transitioning to online workshops presented several difficulties around how best to enable students to have meaningful mathematical discussions and collaborate in writing their solutions when working online. We discuss the changes and mitigations we implemented in order to move the workshops online and how this will inform future in-person workshops.

IntroductionDespite the significant number of deaf and hard of hearing (DHH) people living in the U.S., oral health research on DHH people who use American Sign Language (ASL) is virtually nonexistent. This study aims to investigate dental needs among mid-to-older DHH women and identify social determinants of health that may place them at higher risk for unmet dental health needs as the primary outcome.MethodsThis cross-sectional study uses data drawn from Communication Health domain in the PROMIS-DHH Profile and oral health data from the National Health and Nutrition Examination Survey. Both measures were administered in ASL and English between November 2019 and March 2020. Univariate and bivariate analysis included only complete data, and multivariable logistic regression analyses were conducted on multiply imputed data.ResultsOut of 197 DHH women (41 to 71+ years old) who answered the dental visit question, 48 had unmet dental needs and 149 had met dental needs. Adjusting for sociodemographic variables, disparity in dental needs was observed across education [OR (95% CI): 0.45(0.15, 1.370)] and communication health [0.95 (0.90, 1.01)].DiscussionOur study is the first to describe DHH mid-to-older women's access to oral health care. DHH women who do not have a college degree may be impacted. Further research is needed to elucidate the particular risk factors, including cultural, to which DHH individuals from marginalized racial groups are susceptible to unmet oral health needs.ConclusionsEvidence shows that DHH ASL users who have less years of education or are single experience barriers in accessing dental care.

Let D be a diagram of an alternating knot with unknotting number one. The branched double cover of S 3 branched over D is an L-space obtained by half integral surgery on a knot KD. We denote the set of all such knots KD by D. We characterize when KD ∈ D is a torus knot, a satellite knot or a hyperbolic knot. In a different direction, we show that for a given n > 0, there are only finitely many L-space knots in D with genus less than n.Definition 1.2. Let (D, c) be an alternating diagram with an unknotting crossing c. Let C be a Conway sphere in D, disjoint from the unknotting arc specified by c. We will call the component of 1 An L-space Y is a rational homology sphere with the simplest possible Heegaard Floer invariant, that is rk HF (Y ) = |H1(Y ; Z)|.