The Submanifold Geometries Associated to Grassmannian Systems PDF Download
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Author: Martina Brück
Publisher: American Mathematical Soc.
ISBN: 0821827537
Category : Mathematics
Languages : en
Pages : 111
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Book Description
This work is intended for graduate students and research mathematicians interested in differential geometry and partial differential equations.
Author: Martina Brück
Publisher: American Mathematical Soc.
ISBN: 0821827537
Category : Mathematics
Languages : en
Pages : 111
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Book Description
This work is intended for graduate students and research mathematicians interested in differential geometry and partial differential equations.
Author: Francisco Santos
Publisher: American Mathematical Soc.
ISBN: 0821827693
Category : Mathematics
Languages : en
Pages : 95
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Book Description
We consider the concept of triangulation of an oriented matroid. We provide a definition which generalizes the previous ones by Billera-Munson and by Anderson and which specializes to the usual notion of triangulation (or simplicial fan) in the realizable case. Then we study the relation existing between triangulations of an oriented matroid $\mathcal{M}$ and extensions of its dual $\mathcal{M}^*$, via the so-called lifting triangulations. We show that this duality behaves particularly well in the class of Lawrence matroid polytopes. In particular, that the extension space conjecture for realizable oriented matroids is equivalent to the restriction to Lawrence polytopes of the Generalized Baues problem for subdivisions of polytopes. We finish by showing examples and a characterization of lifting triangulations.
Author: Nanhua Xi
Publisher: American Mathematical Soc.
ISBN: 0821828916
Category : Mathematics
Languages : en
Pages : 114
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Book Description
In this paper we prove Lusztig's conjecture on based ring for an affine Weyl group of type $\tilde A_{n-1}$.
Author: Jürgen Ritter
Publisher: American Mathematical Soc.
ISBN: 0821829289
Category : Mathematics
Languages : en
Pages : 105
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Book Description
This paper concerns the relation between the Lifted Root Number Conjecture, as introduced in [GRW2], and a new equivariant form of Iwasawa theory. A main conjecture of equivariant Iwasawa theory is formulated, and its equivalence to the Lifted Root Number Conjecture is shown subject to the validity of a semi-local version of the Root Number Conjecture, which itself is proved in the case of a tame extension of real abelian fields.
Author: Robert M. Guralnick
Publisher: American Mathematical Soc.
ISBN: 0821832883
Category : Mathematics
Languages : en
Pages : 96
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Book Description
Investigates the analogous question for rational functions. This book describes the Galois theoretic translation, based on Chebotarev's density theorem, leads to a certain property of permutation groups, called exceptionality.
Author: Wojciech Chachólski
Publisher: American Mathematical Soc.
ISBN: 0821827596
Category : Mathematics
Languages : en
Pages : 106
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Book Description
In this paper the authors develop homotopy theoretical methods for studying diagrams. In particular they explain how to construct homotopy colimits and limits in an arbitrary model category. The key concept introduced is that of a model approximation. A model approximation of a category $\mathcal{C}$ with a given class of weak equivalences is a model category $\mathcal{M}$ together with a pair of adjoint functors $\mathcal{M} \rightleftarrows \mathcal{C}$ which satisfy certain properties. The key result says that if $\mathcal{C}$ admits a model approximation then so does the functor category $Fun(I, \mathcal{C})$.
Author: Po Hu
Publisher: American Mathematical Soc.
ISBN: 0821829564
Category : Mathematics
Languages : en
Pages : 141
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Book Description
Gives a theory $S$-modules for Morel and Voevodsky's category of algebraic spectra over an arbitrary field $k$. This work also defines universe change functors, as well as other important constructions analogous to those in topology, such as the twisted half-smash product.
Author: Robert Bieri
Publisher: American Mathematical Soc.
ISBN: 0821831844
Category : Mathematics
Languages : en
Pages : 105
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Book Description
Generalizing the Bieri-Neumann-Strebel-Renz Invariants, this Memoir presents the foundations of a theory of (not necessarily discrete) actions $\rho$ of a (suitable) group $G$ by isometries on a proper CAT(0) space $M$. The passage from groups $G$ to group actions $\rho$ implies the introduction of 'Sigma invariants' $\Sigmak(\rho)$ to replace the previous $\Sigmak(G)$ introduced by those authors. Their theory is now seen as a special case of what is studied here so that readers seeking a detailed treatment of their theory will find it included here as a special case. We define and study 'controlled $k$-connectedness $(CCk)$' of $\rho$, both over $M$ and over end points $e$ in the 'boundary at infinity' $\partial M$; $\Sigmak(\rho)$ is by definition the set of all $e$ over which the action is $(k-1)$-connected. A central theorem, the Boundary Criterion, says that $\Sigmak(\rho) = \partial M$ if and only if $\rho$ is $CC{k-1}$ over $M$.An Openness Theorem says that $CCk$ over $M$ is an open condition on the space of isometric actions $\rho$ of $G$ on $M$. Another Openness Theorem says that $\Sigmak(\rho)$ is an open subset of $\partial M$ with respect to the Tits metric topology. When $\rho(G)$ is a discrete group of isometries the property $CC{k-1}$ is equivalent to ker$(\rho)$ having the topological finiteness property type '$F_k$'. More generally, if the orbits of the action are discrete, $CC{k-1}$ is equivalent to the point-stabilizers having type $F_k$. In particular, for $k=2$ we are characterizing finite presentability of kernels and stabilizers. Examples discussed include: locally rigid actions, translation actions on vector spaces (especially those by metabelian groups
Author: Jie Wu
Publisher: American Mathematical Soc.
ISBN: 0821832395
Category : Mathematics
Languages : en
Pages : 148
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Book Description
Investigates the homotopy theory of the suspensions of the real projective plane. This book computes the homotopy groups up to certain range. It also studies the decompositions of the self smashes and the loop spaces with some applications to the Stiefel manifolds.
Author: Masaki Izumi
Publisher: American Mathematical Soc.
ISBN: 0821829351
Category : Mathematics
Languages : en
Pages : 215
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Book Description
This title deals with a map $\alpha$ from a finite group $G$ into the automorphism group $Aut({\mathcal L})$ of a factor ${\mathcal L}$ satisfying (i) $G=N \rtimes H$ is a semi-direct product, (ii) the induced map $g \in G \to [\alpha_g] \in Out({\mathcal L})=Aut({\mathcal L})/Int({\mathcal L})$ is an injective homomorphism, and (iii) the restrictions $\alpha \! \! \mid_N, \alpha \! \! \mid_H$ are genuine actions of the subgroups on the factor ${\mathcal L}$. The pair ${\mathcal M}={\mathcal L} \rtimes_{\alpha} H \supseteq {\mathcal N}={\mathcal L} DEGREES{\alpha\mid_N}$ (of the crossed product ${\mathcal L} \rtimes_{\alpha} H$ and the fixed-point algebra ${\mathcal L} DEGREES{\alpha\mid_N}$) gives an irreducible inclusion of factors with Jones index $\# G$. The inclusion ${\mathcal M} \supseteq {\mathcal N}$ is of depth $2$ and hence known to correspond to a Kac algebra of dim
