9 research outputs found
cohomology is intersection cohomology
Let be any subanalytic compact pseudomanifold. We show a De Rham theorem
for forms. We prove that the cohomology of forms is
isomorphic to intersection cohomology in the maximal perversity.Comment: Appendix on subanalytic geometry adde
Analytic cell decomposition and analytic motivic integration
The main results of this paper are a Cell Decomposition Theorem for Henselian
valued fields with analytic structure in an analytic Denef-Pas language, and
its application to analytic motivic integrals and analytic integrals over
\FF_q((t)) of big enough characteristic. To accomplish this, we introduce a
general framework for Henselian valued fields with analytic structure, and
we investigate the structure of analytic functions in one variable, defined on
annuli over . We also prove that, after parameterization, definable analytic
functions are given by terms. The results in this paper pave the way for a
theory of \emph{analytic} motivic integration and \emph{analytic} motivic
constructible functions in the line of R. Cluckers and F. Loeser
[\emph{Fonctions constructible et int\'egration motivic I}, Comptes rendus de
l'Acad\'emie des Sciences, {\bf 339} (2004) 411 - 416]
Constructible motivic functions and motivic integration
We introduce a direct image formalism for constructible motivic functions.
One deduces a very general version of motivic integration for which a change of
variables theorem is proved. These constructions are generalized to the
relative framework, in which we develop a relative version of motivic
integration. These results have been announced in math.AG/0403349 and
math.AG/0403350.
Main results and statements unchanged. Many minor slips corrected and some
details added.Comment: Final versio
Cosmological Inflation, Dark Matter and Dark Energy
Various cosmological observations support not only cosmological inflation in the early universe, which is also known as exponential cosmic expansion, but also that the expansion of the late-time universe is accelerating. To explain this phenomenon, the existence of dark energy is proposed. In addition, according to the rotation curve of galaxies, the existence of dark matter, which does not shine, is also suggested. If primordial gravitational waves are detected in the future, the mechanism for realizing inflation can be revealed. Moreover, there exist two main candidates for dark matter. The first is a new particle, the existence of which is predicted in particle physics. The second is an astrophysical object which is not found by electromagnetic waves. Furthermore, there are two representative approaches to account for the accelerated expansion of the current universe. One is to assume the unknown dark energy in general relativity. The other is to extend the gravity theory to large scales. Investigation of the origins of inflation, dark matter, and dark energy is one of the most fundamental problems in modern physics and cosmology. The purpose of this book is to explore the physics and cosmology of inflation, dark matter, and dark energy