Homology manifold bordism

The Bryant-Ferry-Mio-Weinberger surgery exact sequence for compact homology manifolds of dimension is used to obtain transversality, splitting and bordism results for homology manifolds, generalizing previous work of Johnston.

First, we establish homology manifold transversality for submanifolds of dimension : if is a map from an -dimensional homology manifold to a space , and is a subspace with a topological -block bundle neighborhood, and , then is homology manifold -cobordant to a map which is transverse to , with an -dimensional homology submanifold.

Second, we obtain a codimension splitting obstruction in the Wall -group for a simple homotopy equivalence from an -dimensional homology manifold to an -dimensional Poincaré space with a codimension Poincaré subspace with a topological normal bundle, such that if (and for only if) splits at up to homology manifold -cobordism.

Third, we obtain the multiplicative structure of the homology manifold bordism groups .

     

On the structure of Fatou domains

Let U be a multiply-connected fixed attracting Fatou domain of a rational map f.We prove that there exist a rational map g and a completely invariant Fatou domain V of g such that(f,U) and(g,V) are holomorphically conjugate,and each non-trivial Julia component of g is a quasi-circle which bounds an eventually superattracting Fatou domain of g containing at most one postcritical point of g.Moreover,g is unique up to a holomorphic conjugation.     

Codimension Two PL Embeddings of Spheres with Nonstandard Regular Neighborhoods

For a given polyhedron K(?)M,the notation RM(K)denotes a regular neigh- borhood of K in M.The authors study the following problem:find all pairs(m,k) such that if K is a compact k-polyhedron and M a PL m-manifold,then R_M(f(K))≌R_M(g(K))for each two homotopic PL embeddings f,g:K→M.It is proved that R_S~(k 2)(S~k)(?)S~k×D~2 for each k(?)2 and some PL sphere S~k(?)S~(k 2)(even for any PL sphere S~k(?)S~(K 2)having an isolated non-locally flat point with the singularity S~(k-1)(?) S~(k 1)such thatπ_1(S~(k 1)-S~(k-1))(?)Z).     

Decision problems in the space of Dehn fillings

Normal surface theory is used to study Dehn fillings of a knot-manifold. We use that any triangulation of a knot-manifold may be modified to a triangulation having just one vertex in the boundary. In this situation, it is shown that there is a finite computable set of slopes on the boundary of the knot-manifold, which come from boundary slopes of normal or almost normal surfaces. This is combined with existence theorems for normal and almost normal surfaces to construct algorithms to determine precisely those manifolds obtained by Dehn filling of a given knot-manifold that: (1) are reducible, (2) contain two-sided incompressible surfaces, (3) are Haken, (4) fiber over S¹, (5) are the 3-sphere, and (6) are a lens space. Each of these algorithms is a finite computation.Moreover, in the case of essential surfaces, we show that the topology of each filled manifold is strongly reflected in the combinatorial properties of a triangulation of the knot-manifold with just one vertex in the boundary. If a filled manifold contains an essential surface then the knot-manifold contains an essential normal vertex solution which caps off to an essential surface of the same type in the filled manifold. (Normal vertex solutions are the premier class of normal surface and are computable.)     

Visible surgery, four-dimensionals-cobordisms and related questions in geometric topology

The visible surgery theory of M. Weiss is used to complete the topological classification of four-dimensionals-cobordisms between three-dimensional spherical spaceforms. Applications to various questions concerning pseudo-isotopies of 3-manifolds, computations of the simple Wall groups of finite periodic groups, and inductive detection of self-homeomorphisms of manifolds are also discussed.The first named author was partially supported by a grant from the Louisiana Board of Regents and National Science Foundation Grants DMS 89-01583 and 91-01575, and the second named author was partially supported by National Science Foundation Grants DMS 86-02543, 89-02622 and 91-02711.     

超声刀在甲状腺手术中保护喉返神经及入喉处甲状腺组织的应用效果观察

目的探讨超声刀在甲状腺手术中对于喉返神经及入喉处甲状腺组织的保护作用。方法选取2016年1月至12月间广东省遂溪县人民医院收治的120例甲状腺疾病的患者,随机分为对照组和观察组,每组60例,对照组采用传统电刀手术,观察组采用超声刀进行手术,比较两种手术方式的效果以及对喉返神经及入喉处甲状腺组织的影响。结果相较于传统电刀手术,采用超声刀可明显缩短腺体切除时间和手术总时间,减少术中出血量,差异具有统计学意义(P0.05);两种手术方式在术后引流量和住院时间方面比较,差异无统计学意义(P0.05);观察组患者喉返神经损伤以及甲状旁腺功能低下的发生率低于对照组,但是两组间差异无统计学意义(P0.05),所有观察组患者的声音嘶哑现象均于术后3个月内恢复,而对照组有3例于3~6个月恢复,2例1年以上未好转。结论在甲状腺手术最终采用超声刀可明显缩短手术时间,减少术中出血量,利于术中对喉返神经和入喉处甲状腺组织的辨认和保护,是一种安全可行的手术方法。     

Reverse Thermal Gel for In Utero Coverage of Spina Bifida Defects: An Innovative Bioengineering Alternative to Open Fetal Repair

Current state‐of‐the‐art management of open spina bifida defects entails an open fetal surgery approach associated with significant morbidities. In an attempt to reduce these risks and provide for an earlier minimally invasive repair, it is aimed to develop and characterize an innovative alternative using a unique reverse thermal gel. This study focuses on characterization of the physical and biological properties of the polymer and its in vivo applicability. Based on the knowledge and benchmarking, the “ideal” biomaterial should have the following characteristics: stability in amniotic fluid, limited permeability, biocompatibility, biologically functional, nontoxic, ability to support cellular functions, and in vivo applicability. The results demonstrate that the polymer possesses a unique ultrastructure, is stable in amniotic fluid, possesses limited yet predictable permeability, biocompatible with cells exposed in neural tube defects, is nontoxic, and can support cellular migration. These characteristics make it a potential novel alternative to open fetal repairs.

     

Semi-invariants in surgery

A semi-invariant in surgery is an invariant of a quadratic Poincaré complex which is defined in terms of a null-cobordism. We define five such gadgets: the semicharacteristic, the semitorsion, the cross semitorsion, the torsion semicharacteristic, and the cross torsion semicharacteristic. We describe applications to the evaluation of surgery obstructions, especially in the odd-dimensional case.     

Nonspecific laryngeal granuloma: A case study of a professional singer

A professional singer with laryngeal granuloma underwent surgery following failed response to conservative treatments. Two primary findings emerged. First, although a sizable lesion was present initially, presurgical voice measures were largely normal or superior. The exception was elevated phonatory effort during singing. Second, postsurgical voice functions were entirely normal or superior (including phonatory effort), despite demanding singing performances a few weeks following surgery. The results add to the limited corpus of quantitative, normative-referenced data on voice in patients with granulomas and are inconsistent with previous reports of voice abnormalities in such patients and poor functional response to surgery.