Related papers: Notes on the Sigma invariants

We show how the sine and cosine integrals may be usefully employed in the evaluation of some more complex integrals.

Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.

In the previous article we introduced the new concept of mixed representations of quivers and described the generators of their algebras of invariants. In this article we describe the defining relations of these algebras. Some applications…

This is the second part of the paper "A degeneration of stable morphisms and relative stable morphisms", (math.AG/0009097). In this paper, we constructed the relative Gromov-Witten invariants of a pair of a smooth variety and a smooth…

This is the second of a series of two technical papers devoted to the analysis of holonomy invariants in strict higher gauge theory with end applications in higher Chern--Simons theory. We provide a definition of trace over a crossed module…

Let $(M,g)$ be a compact Riemannian manifold of dimension $n \geq 3$. We define the second Yamabe invariant as the infimum of the second eigenvalue of the Yamabe operator over the metrics conformal to $g$ and of volume 1. We study when it…

This is an English translation of the expository article written by the author in Japanese for publication in {\em Sugaku}. The author will explain Milnor invariants from the viewpoint of his research.

This unpublished paper is a copy (completed by a development of section 5 and by minor corrections) of the article with the same title published in: Complex Analysis and Digital Geometry, Proceedings from the Kiselmanfest, 2006, Acta…

In this note, we address the doubts of Singh (2001) and Gupta and Shabbir (2008) on the transformations of auxiliary variables by adding unit free constants. The original contribution by Sisodia and Dwivedi (1981) is correct.

We construct a family of representations of an arbitrary variant $S_a$ of a semigroup $S$, induced by a given representation of $S$, and investigate properties of such representations and their kernels.

These notes survey some basic results in toric varieties over a field with examples and applications. A computer algebra package (written by the second author) is described which deals with both affine and projective toric varieties in any…

This is a survey article on finite type invariants of 3-manifolds written for the Encyclopedia of Mathematical Physics to be published by Elsevier.

Series of short contributions that are part of Nobel Symposium 162 - Microfluidics arXiv:1712.08369.

Some formulas and speculations are presented relative to integrable systems and quantum mechanics.

This version has been withdrawn. The new and final version is on ArXiv 1103.4878

Section I contains introductory remarks about surface motions. Section II gives a detailed derivation of $H=-\Delta-Tr\sum_{i<j}[X_i,X_j]^2$ as describing a quantized discrete analogue of relativistically invariant membrane dynamics.…

We present an explicit expression for the topological invariants associated to $SU(2)$ monopoles in the fundamental representation on spin four-manifolds. The computation of these invariants is based on the analysis of their corresponding…

These notes cover background material on trees which are used in the paper `On uniqueness of the signature of a path of variation and the reduced path group'.

This note describes an invariant of rational homology 3-spheres in terms of configuration space integrals which in some sense lies between the invariants of Axelrod and Singer and those of Kontsevich.

We discuss additional supersymmetries for N = (2, 2) supersymmetric non-linear sigma models described by left and right semichiral superfields.