Author : Dan Haran
Publisher : American Mathematical Soc.
Page : 70 pages
File Size : 49,97 MB
Release : 2007
Category : Mathematics
ISBN : 0821839950
The authors prove: A proper profinite group structure G is projective if and only if G is the absolute Galois group structure of a proper field-valuation structure with block approximation.
Author : Dan Haran
Publisher : American Mathematical Soc.
Page : 56 pages
File Size : 34,90 MB
Release : 2007
Category : Mathematics
ISBN : 9781470404888
Proves that a proper profinite group structure $\mathbf{G}$ is projective if and only if $\mathbf{G}$ is the absolute Galois group structure of a proper field-valuation structure with block approximation.
Author : Yuanhua Wang
Publisher : American Mathematical Soc.
Page : 104 pages
File Size : 35,76 MB
Release : 2008
Category : Mathematics
ISBN : 0821841661
The purpose of this paper is to establish the spinor genus theory of quadratic forms over global function fields in characteristic 2. The first part of the paper computes the integral spinor norms and relative spinor norms. The second part of the paper gives a complete answer to the integral representations of one quadratic form by another with more than four variables over a global function field in characteristic 2.
Author : Ron Donagi
Publisher : American Mathematical Soc.
Page : 104 pages
File Size : 22,5 MB
Release : 2008
Category : Mathematics
ISBN : 0821840924
Let $X$ be a smooth elliptic fibration over a smooth base $B$. Under mild assumptions, the authors establish a Fourier-Mukai equivalence between the derived categories of two objects, each of which is an $\mathcal{O} DEGREES{\times}$ gerbe over a genus one fibration which is a twisted form
Author : Raphael Ponge
Publisher : American Mathematical Soc.
Page : 150 pages
File Size : 48,9 MB
Release : 2008
Category : Mathematics
ISBN : 0821841483
This memoir deals with the hypoelliptic calculus on Heisenberg manifolds, including CR and contact manifolds. In this context the main differential operators at stake include the Hormander's sum of squares, the Kohn Laplacian, the horizontal sublaplacian, the CR conformal operators of Gover-Graham and the contact Laplacian. These operators cannot be elliptic and the relevant pseudodifferential calculus to study them is provided by the Heisenberg calculus of Beals-Greiner andTaylor.
Author : Cameron Gordon
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 29,72 MB
Release : 2008
Category : Mathematics
ISBN : 082184167X
The authors determine all hyperbolic $3$-manifolds $M$ admitting two toroidal Dehn fillings at distance $4$ or $5$. They show that if $M$ is a hyperbolic $3$-manifold with a torus boundary component $T 0$, and $r,s$ are two slopes on $T 0$ with $\Delta(r,s) = 4$ or $5$ such that $M(r)$ and $M(s)$ both contain an essential torus, then $M$ is either one of $14$ specific manifolds $M i$, or obtained from $M 1, M 2, M 3$ or $M {14}$ by attaching a solid torus to $\partial M i - T 0$.All the manifolds $M i$ are hyperbolic, and the authors show that only the first three can be embedded into $S3$. As a consequence, this leads to a complete classification of all hyperbolic knots in $S3$ admitting two toroidal surgeries with distance at least $4$.
Author : Gail Letzter
Publisher : American Mathematical Soc.
Page : 104 pages
File Size : 18,37 MB
Release : 2008
Category : Mathematics
ISBN : 0821841319
This paper studies quantum invariant differential operators for quantum symmetric spaces in the maximally split case. The main results are quantum versions of theorems of Harish-Chandra and Helgason: There is a Harish-Chandra map which induces an isomorphism between the ring of quantum invariant differential operators and the ring of invariants of a certain Laurent polynomial ring under an action of the restricted Weyl group. Moreover, the image of the center under this map is the entire invariant ring if and only if the underlying irreducible symmetric pair is not of four exceptional types. In the process, the author finds a particularly nice basis for the quantum invariant differential operators that provides a new interpretation of difference operators associated to Macdonald polynomials.
Author : Dominic Verity
Publisher : American Mathematical Soc.
Page : 208 pages
File Size : 12,42 MB
Release : 2008
Category : Mathematics
ISBN : 0821841424
The primary purpose of this work is to characterise strict $\omega$-categories as simplicial sets with structure. The author proves the Street-Roberts conjecture in the form formulated by Ross Street in his work on Orientals, which states that they are exactly the ``complicial sets'' defined and named by John Roberts in his handwritten notes of that title (circa 1978). On the way the author substantially develops Roberts' theory of complicial sets itself and makes contributions to Street's theory of parity complexes. In particular, he studies a new monoidal closed structure on the category of complicial sets which he shows to be the appropriate generalisation of the (lax) Gray tensor product of 2-categories to this context. Under Street's $\omega$-categorical nerve construction, which the author shows to be an equivalence, this tensor product coincides with those of Steiner, Crans and others.
Author : Piotr Hajłasz
Publisher : American Mathematical Soc.
Page : 88 pages
File Size : 35,77 MB
Release : 2008
Category : Mathematics
ISBN : 0821840797
The authors study Sobolev classes of weakly differentiable mappings $f: {\mathbb X}\rightarrow {\mathbb Y}$ between compact Riemannian manifolds without boundary. These mappings need not be continuous. They actually possess less regularity than the mappings in ${\mathcal W}{1, n}({\mathbb X}\, \, {\mathbb Y})\, $, $n=\mbox{dim}\, {\mathbb X}$. The central themes being discussed a
Author : Sergey Zelik
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 38,9 MB
Release : 2009-03-06
Category : Mathematics
ISBN : 0821842641
The authors study semilinear parabolic systems on the full space ${\mathbb R}^n$ that admit a family of exponentially decaying pulse-like steady states obtained via translations. The multi-pulse solutions under consideration look like the sum of infinitely many such pulses which are well separated. They prove a global center-manifold reduction theorem for the temporal evolution of such multi-pulse solutions and show that the dynamics of these solutions can be described by an infinite system of ODEs for the positions of the pulses. As an application of the developed theory, The authors verify the existence of Sinai-Bunimovich space-time chaos in 1D space-time periodically forced Swift-Hohenberg equation.
