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Prosthetic joint infection (PJI) is a devastating complication in total knee arthroplasty (TKA) and third most common cause of revision of TKA with significant morbidity and surgical challenges. Treatment options include non-operative measures with long term antibiotic suppression, debridement and implant retention (DAIR), one- or two-stage revision arthroplasty, arthrodesis and amputation. Implant retention without infection is ideal and DAIR has been reported to have variable success rates depending on patient factors, duration of infection, infecting micro-organisms, choice of procedure, single or multiple debridement procedures, arthroscopic or open, antibiotic choice and duration of antibiotic use. We present a thorough literature review of DAIR for infected TKA. The important factors contributing to failure are presence of sinus, immunocompromised patient, delay between onset of infection and debridement procedure, Staphylococcal infection in particular Meticillin Resistant Staphylococcal aureus, multiple debridement procedures, retention of exchangeable components and short antibiotic duration. In conclusion DAIR can be successful procedure to eradicate infection in TKA in selective patients with factors contributing to failure taken into account.

We classify hyperbolic polynomials in two real variables that admit a transitive action on some component of their hyperbolic level sets. Such surfaces are called special homogeneous surfaces, and they are equipped with a natural Riemannian metric obtained by restricting the negative Hessian of their defining polynomial. Independent of the degree of the polynomials, there exist a finite number of special homogeneous surfaces. They are either flat, or have constant negative curvature.

We introduce an analogue in hyperkähler geometry of the symplectic implosion, in the case of $\\mathrm{SU} (n)$ actions. Our space is a stratified hyperkähler space which can be defined in terms of quiver diagrams. It also has a description as a non-reductive geometric invariant theory quotient.

We introduce an analogue in hyperkaehler geometry of the symplectic implosion, in the case of actions. Our space is a stratified hyperkaehler space which can be defined in terms of quiver diagrams. It also has a description as a non-reductive geometric invariant theory quotient.

We classify hyperbolic polynomials in two real variables that admit a transitive action on some component of their hyperbolic level sets. Such surfaces are called special homogeneous surfaces, and they are equipped with a natural Riemannian metric obtained by restricting the negative Hessian of their defining polynomial. Independent of the degree of the polynomials, there exist a finite number of special homogeneous surfaces. They are either flat, or have constant negative curvature.

We study the hypersymplectic spaces obtained as quotients of flat hypersymplectic space R4d\\mathbb {R}^{4d} by the action of a compact Abelian group. These 4n4n-dimensional quotients carry a multi-Hamilitonian action of an nn-torus. The image of the hypersymplectic moment map for this torus action may be described by a configuration of solid cones in R3n\\mathbb {R}^{3n}. We give precise conditions for smoothness and non-degeneracy of such quotients and show how some properties of the quotient geometry and topology are constrained by the combinatorics of the cone configurations. Examples are studied, including non-trivial structures on R4n\\mathbb {R}^{4n} and metrics on complements of hypersurfaces in compact manifolds.

We study the projective special Kaehler condition on groups, providing an intrinsic definition of homogeneous projective special Kaehler that includes the previously known examples. We give intrinsic defining equations that may be used without resorting to computations in the special cone, and emphasise certain associated integrability equations. The definition is shown to have the property that the image of such structures under the c-map is necessarily a left-invariant quaternionic Kaehler structure on a Lie group.

We study complete, simply-connected manifolds with special holonomy that are toric with respect to their multi-moment maps. We consider the cases where there is a connected non-Abelian symmetry group containing the torus. For \\(\\mathrm{Spin}(7)\\)-manifolds, we show that the only possibility are structures with a cohomogeneity-two action of \\(T^{3} \\times \\mathrm{SU}(2)\\). We then specialise the analysis to holonomy \\(G_{2}\\), to Calabi-Yau geometries in real dimension six and to hyperK\"ahler four-manifolds. Finally, we consider weakly coherent triples on \\(\\mathbb{R} \\times \\mathrm{SU}(2)\\), and their extensions over singular orbits, to give local examples in the \\(\\mathrm{Spin}(7)\\)-case that have singular orbits where the stabiliser is of rank one.

We consider nearly K\"ahler 6-manifolds with effective 2-torus symmetry. The multi-moment map for the \\(T^2\\)-action becomes an eigenfunction of the Laplace operator. At regular values, we prove the \\(T^2\\)-action is necessarily free on the level sets and determines the geometry of three-dimensional quotients. An inverse construction is given locally producing nearly K\"ahler six-manifolds from three-dimensional data. This is illustrated for structures on the Heisenberg group.