32,995 research outputs found
A Functor Converting Equivariant Homology to Homotopy
In this paper, we prove an equivariant version of the classical Dold-Thom
theorem. Associated to a finite group, a CW-complex on which this group acts
and a covariant coefficient system in the sense of Bredon, we functorially
construct a topological abelian group by the coend construction. Then we prove
that the homotopy groups of this topological abelian group are naturally
isomorphic to the Bredon equivariant homology of the CW-complex. At the end we
present several examples of this result.Comment: 11 pages. Major style change. The final published versio
Polynomial Optimization with Real Varieties
We consider the optimization problem of minimizing a polynomial f(x) subject
to polynomial constraints h(x)=0, g(x)>=0. Lasserre's hierarchy is a sequence
of sum of squares relaxations for finding the global minimum. Let K be the
feasible set. We prove the following results: i) If the real variety V_R(h) is
finite, then Lasserre's hierarchy has finite convergence, no matter the complex
variety V_C(h) is finite or not. This solves an open question in Laurent's
survey. ii) If K and V_R(h) have the same vanishing ideal, then the finite
convergence of Lasserre's hierarchy is independent of the choice of defining
polynomials for the real variety V_R(h). iii) When K is finite, a refined
version of Lasserre's hierarchy (using the preordering of g) has finite
convergence.Comment: 12 page
Subtle Features in Transport Properties: Evidence for a Possible Coexistence of Holes and Electrons in Cuprate Superconductors
Transport properties of high transition temperature (high Tc) cuprate
superconductors are investigated within a two-band model. The doping dependent
Hall coefficients of La_{2-x}Sr_xCuO_4 (LSCO) and Nd_{2-x}Ce_xCuO_4 (NCCO) are
explained by assuming the coexistence of two carriers with opposite charges,
loosely speaking electrons (e) and holes (h). Such a possible electron-hole
coexistence (EHC) in other p-type cuprates is also inferred from subtle
features in the Hall coefficient R_H and thermopower S. The EHC possibly
relates to the pseudogap and sign reversals of transport coefficients near Tc.
It also corroborates the electronlike Fermi surface revealed in recent
photoemission results. An experimental verification is proposed.Comment: 4 pages, 3 EPS figures. RevTe
Entropy degeneration of convex projective surfaces
We show that the volume entropy of the Hilbert metric on a closed convex
projective surface tends to zero as the corresponding Pick differential tends
to infinity. The proof is based on the theorem, due to Benoist and Hulin, that
the Hilbert metric and Blaschke metric are comparable.Comment: 5 page
Solving Toda field theories and related algebraic and differential properties
Toda field theories are important integrable systems. They can be regarded as
constrained WZNW models, and this viewpoint helps to give their explicit
general solutions, especially when a Drinfeld-Sokolov gauge is used. The main
objective of this paper is to carry out this approach of solving the Toda field
theories for the classical Lie algebras. In this process, we discover and prove
some algebraic identities for principal minors of special matrices. The known
elegant solutions of Leznov fit in our scheme in the sense that they are the
general solutions to our conditions discovered in this solving process. To
prove this, we find and prove some differential identities for iterated
integrals. It can be said that altogether our paper gives complete mathematical
proofs for Leznov's solutions
Topologically slice -knots which are not smoothly slice
We prove that there are infinitely many -knots which are topologically
slice, but not smoothly slice, which was a conjecture proposed by B\'ela
Andr\'as R\'acz.Comment: 11 pages, 12 figure
Fundamental elements of an affine Weyl group
Fundamental elements are certain special elements of affine Weyl groups
introduced by Gortz, Haines, Kottwitz and Reuman. They play an important role
in the study of affine Deligne-Lusztig varieties. In this paper, we obtain
characterizations of the fundamental elements and their natural
generalizations. We also derive an inverse to a version of "Newton-Hodge
decomposition" in affine flag varieties. As an application, we obtain a
group-theoretic generalization of Oort's results on minimal p-divisible groups,
and we show that, in certain good reduction reduction of PEL Shimura datum,
each Newton stratum contains a minimal Ekedahl-Oort stratum. This generalizes a
result of Viehmann and Wedhorn.Comment: Some applications to good reductions of PEL shimura varieties are
adde
Indeterminacy Loci of Iterate Maps
We consider the indeterminacy locus of the iterate map
, where is
the GIT compactification of the moduli space of degree complex
rational maps. We give natural conditions on that imply .
These provide partial answers to a question of Laura DeMarco
Certifying Convergence of Lasserre's Hierarchy via Flat Truncation
This paper studies how to certify the convergence of Lasserre's hierarchy of
semidefinite programming relaxations for solving multivariate polynomial
optimization. We propose flat truncation as a general certificate for this
purpose. Assume the set of global minimizers is nonempty and finite. Our main
results are: i) Putinar type Lasserre's hierarchy has finite convergence if and
only if flat truncation holds, under some general assumptions, and this is also
true for the Schmudgen type one; ii) under the archimedean condition, flat
truncation is asymptotically satisfied for Putinar type Lasserre's hierarchy,
and similar is true for the Schmudgen type one; iii) for the hierarchy of
Jacobian SDP relaxations, flat truncation is always satisfied. The case of
unconstrained polynomial optimization is also discussed.Comment: 18 page
Secondary Chern-Euler class for general submanifold
We define and study the secondary Chern-Euler class for a general submanifold
of a Riemannian manifold. Using this class, we define and study index for a
vector field with non-isolated singularities on a submanifold. As an
application, our studies give conceptual proofs of a classical result of Chern.Comment: Section 2 expanded and fixed. Final version to appear in Canadian
Mathematical Bulleti
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