Abstract:
Objectives. Heparin replacement (HR) is often performed in patients with a high risk of thrombosis undergoing endoscopic procedures. However, information about the influence of HR is scarce. The aim of this study is to assess the clinical impact of HR for gastric endoscopic submucosal dissection (ESD). Methods. This is a retrospective study comprising approximately 1310 consecutive gastric neoplasms in 1250 patients, who underwent ESD in 5 institutes. We assessed the clinical findings and outcomes of ESD under HR, compared to ESD without HR as control. Results. A total of 24 EGC lesions in 24 patients were treated by ESD under HR. In the HR group, the complete en-bloc resection rate was 100%. The delayed bleeding rate was, however, higher in the HR group than in the controls (38% versus 4.6%). The timing of bleeding in the HR group was significantly later than in controls. In the control group, 209 patients discontinued antithrombotic therapy during perioperative period, and their delayed bleeding rate was not different from those without antithrombotic therapy (5.7% versus. 4.4%). A thromboembolic event was encountered in 1 patient under HR after delayed bleeding. Conclusion. ESD under HR is technically feasible but has a high risk of delayed bleeding. 1. Introduction Endoscopic resection of early gastric cancer (EGC) started as endoscopic mucosal resection (EMR) [1] and has dramatically developed and been applied in many patients, owing to the establishment of criteria for node-negative tumors [2] and the advancements of endoscopic submucosal dissection (ESD) [3–6]. We recently reported, in a multicenter study, that ESD is a feasible method for treating EGC [7] and that long-term outcome of gastric ESD is satisfactory [8]. We also showed that almost all recurrent lesions, synchronous or metachronous, were treatable by endoscopic resection by scheduled endoscopic surveillance [8]. ESD has become a more acceptable option for EGC than gastrectomy in elderly patients, who often have several comorbidities [9] and accompanying medication such as antithrombogenic agents for the primary and secondary prevention of cerebrovascular and cardiovascular diseases. Some patients with comorbidities such as valvular heart disease, atrial fibrillation with history of cerebrovascular accident have a high risk of developing thrombotic disease. Discontinuation of antithrombotic agents in these patients may cause life-threatening cerebrovascular and cardiovascular events. Such patients are often treated under heparin replacement (HR) of antithrombotic drugs, as a bridge

Abstract:
We construct geometrically a gerbe assigned to a connection on a principal SU(2)-bundle over an oriented closed 1-dimensional manifold. If the connection is given by the restriction of a connection on a bundle over a compact 2-manifold bounding the 1-manifold, then we have a natural object in the gerbe. The gerbes and the objects satisfy certain fundamental properties, e.g. gluing law.

Abstract:
From a certain strongly equivariant bundle gerbe with connection and curving over a smooth manifold on which a Lie group acts, we construct under some conditions a bundle gerbe with connection and curving over the quotient space. In general, the construction requires a choice, and we can consequently obtain distinct stable isomorphism classes of bundle gerbes with connection and curving over the quotient space. A bundle gerbe naturally arising in Chern-Simons theory provides an example of the reduction.

Abstract:
We construct projective unitary representations of the smooth Deligne cohomology group of a compact oriented Riemannian manifold of dimension 4k+1, generalizing positive energy representations of the loop group of the circle. We also classify such representations under a certain condition. The number of the equivalence classes of irreducible representations is finite, and is determined by the cohomology of the manifold.

Abstract:
Based on projective representations of smooth Deligne cohomology groups, we introduce an analogue of the space of conformal blocks to compact oriented (4k+2)-dimensional Riemannian manifolds with boundary. For the standard (4k+2)-dimensional disk, we compute the space concretely to prove that its dimension is finite.

Abstract:
For twisted K-theory whose twist is classified by a degree three integral cohomology of infinite order, universal even degree characteristic classes are in one to one correspondence with invariant polynomials of Atiyah and Segal. The present paper describes the ring of these invariant polynomials by a basis and structure constants.

Abstract:
Mickelsson's invariant is an invariant of certain odd twisted K-classes of compact oriented three dimensional manifolds. We reformulate the invariant as a natural homomorphism taking values in a quotient of the third cohomology, and provide a generalization taking values in a quotient of the fifth cohomology. These homomorphisms are related to the Atiyah-Hirzebruch spectral sequence. We also construct some characteristic classes for odd twisted K-theory in a similar vein.

Abstract:
A twist is a datum playing a role of a local system for topological K-theory. In equivariant setting, twists are classified into four types according to how they are realized geometrically. This paper lists the possible types of twists for the torus with the actions of the point groups of all the 2-dimensional space groups (crystallographic groups), or equivalently, the torus with the actions of all the possible finite subgroups in its mapping class group. This is carried out by computing Borel's equivariant cohomology and the Leray-Serre spectral sequence. As a byproduct, the equivariant cohomology up to degree three is determined in all cases.

Abstract:
We construct a connection and a curving on a bundle gerbe associated with lifting a structure group of a principal bundle to a central extension. The construction is based on certain structures on the bundle, i.e. connections and splittings. The Deligne cohomology class of the lifting bundle gerbe with the connection and with the curving coincides with the obstruction class of the lifting problem with these structures.

Abstract:
We formulate the Chern-Simons action for any compact Lie group using Deligne cohomology. This action is defined as a certain function on the space of smooth maps from the underlying 3-manifold to the classifying space for principal bundles. If the 3-manifold is closed, the action is a function with values in complex numbers. If the 3-manifold is not closed, then the action is a section of a Hermitian line bundle associated with the Riemann surface which appears as the boundary.