560 research outputs found
Torsion, TQFT, and Seiberg-Witten invariants of 3-manifolds
We prove a conjecture of Hutchings and Lee relating the Seiberg-Witten
invariants of a closed 3-manifold X with b_1 > 0 to an invariant that `counts'
gradient flow lines--including closed orbits--of a circle-valued Morse function
on the manifold. The proof is based on a method described by Donaldson for
computing the Seiberg-Witten invariants of 3-manifolds by making use of a
`topological quantum field theory,' which makes the calculation completely
explicit. We also realize a version of the Seiberg-Witten invariant of X as the
intersection number of a pair of totally real submanifolds of a product of
vortex moduli spaces on a Riemann surface constructed from geometric data on X.
The analogy with recent work of Ozsvath and Szabo suggests a generalization of
a conjecture of Salamon, who has proposed a model for the Seiberg-Witten-Floer
homology of X in the case that X is a mapping torus.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol6/paper2.abs.htm
Brauer group of moduli spaces of pairs
We show that the Brauer group of any moduli space of stable pairs with fixed
determinant over a curve is zero.Comment: 12 pages. Final version, accepted in Communications in Algebr
Moduli spaces of coherent systems of small slope on algebraic curves
Let be an algebraic curve of genus . A coherent system on
consists of a pair , where is an algebraic vector bundle over of
rank and degree and is a subspace of dimension of the space of
sections of . The stability of the coherent system depends on a parameter
. We study the geometry of the moduli space of coherent systems for
. We show that these spaces are irreducible whenever they are
non-empty and obtain necessary and sufficient conditions for non-emptiness.Comment: 27 pages; minor presentational changes and typographical correction
Quaternionic Monopoles
We present the simplest non-abelian version of Seiberg-Witten theory:
Quaternionic monopoles. These monopoles are associated with
Spin^h(4)-structures on 4-manifolds and form finite-dimensional moduli spaces.
On a Kahler surface the quaternionic monopole equations decouple and lead to
the projective vortex equation for holomorphic pairs. This vortex equation
comes from a moment map and gives rise to a new complex-geometric stability
concept. The moduli spaces of quaternionic monopoles on Kahler surfaces have
two closed subspaces, both naturally isomorphic with moduli spaces of
canonically stable holomorphic pairs. These components intersect along
Donaldsons instanton space and can be compactified with Seiberg-Witten moduli
spaces. This should provide a link between the two corresponding theories.
Notes: To appear in CMP The revised version contains more details concerning
the Uhlenbeck compactfication of the moduli space of quaternionic monopoles,
and possible applications are discussed. Attention ! Due to an ununderstandable
mistake, the duke server had replaced all the symbols "=" by "=3D" in the
tex-file of the revised version we sent on February, the 2-nd. The command
"\def{\ad}" had also been damaged !Comment: LaTeX, 35 page
Promises and Lies: Restoring Violated Trust
Trust is critical for organizations, effective management, and efficient negotiations, yet trust violations are common. Prior work has often assumed trust to be fragileâeasily broken and difficult to repair. We investigate this proposition in a laboratory study and find that trust harmed by untrustworthy behavior can be effectively restored when individuals observe a consistent series of trustworthy actions. Trust harmed by the same untrustworthy actions and deception, however, never fully recoversâeven when deceived participants receive a promise, an apology, and observe a consistent series of trustworthy actions. We also find that a promise to change behaviour can significantly speed the trust recovery process, but prior deception harms the effectiveness of a promise in accelerating trust recovery
Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces
Higgs bundles and non-abelian Hodge theory provide holomorphic methods with
which to study the moduli spaces of surface group representations in a
reductive Lie group G. In this paper we survey the case in which G is the
isometry group of a classical Hermitian symmetric space of non-compact type.
Using Morse theory on the moduli spaces of Higgs bundles, we compute the number
of connected components of the moduli space of representations with maximal
Toledo invariant.Comment: v2: added due credits to the work of Burger, Iozzi and Wienhard. v3:
corrected count of connected components for G=SU(p,q) (p \neq q); added due
credits to the work of Xia and Markman-Xia; minor corrections and
clarifications. 31 page
Closed-Form Bayesian Inferences for the Logit Model via Polynomial Expansions
Articles in Marketing and choice literatures have demonstrated the need for
incorporating person-level heterogeneity into behavioral models (e.g., logit
models for multiple binary outcomes as studied here). However, the logit
likelihood extended with a population distribution of heterogeneity doesn't
yield closed-form inferences, and therefore numerical integration techniques
are relied upon (e.g., MCMC methods).
We present here an alternative, closed-form Bayesian inferences for the logit
model, which we obtain by approximating the logit likelihood via a polynomial
expansion, and then positing a distribution of heterogeneity from a flexible
family that is now conjugate and integrable. For problems where the response
coefficients are independent, choosing the Gamma distribution leads to rapidly
convergent closed-form expansions; if there are correlations among the
coefficients one can still obtain rapidly convergent closed-form expansions by
positing a distribution of heterogeneity from a Multivariate Gamma
distribution. The solution then comes from the moment generating function of
the Multivariate Gamma distribution or in general from the multivariate
heterogeneity distribution assumed.
Closed-form Bayesian inferences, derivatives (useful for elasticity
calculations), population distribution parameter estimates (useful for
summarization) and starting values (useful for complicated algorithms) are
hence directly available. Two simulation studies demonstrate the efficacy of
our approach.Comment: 30 pages, 2 figures, corrected some typos. Appears in Quantitative
Marketing and Economics vol 4 (2006), no. 2, 173--20
Moduli of ADHM Sheaves and Local Donaldson-Thomas Theory
The ADHM construction establishes a one-to-one correspondence between framed
torsion free sheaves on the projective plane and stable framed representations
of a quiver with relations in the category of complex vector spaces. This paper
studies the geometry of moduli spaces of representations of the same quiver
with relations in the abelian category of coherent sheaves on a smooth complex
projective curve . In particular it is proven that this moduli space is
virtually smooth and related byrelative Beilinson spectral sequence to the
curve counting construction via stable pairs of Pandharipande and Thomas. This
yields a new conjectural construction for the local Donaldson-Thomas theory of
curves as well as a natural higher rank generalization.Comment: 61 pages AMS Latex; v2: minor corrections, reference added; v3: some
proofs corrected using the GIT construction of the moduli space due to A.
Schmitt; main results unchanged; final version to appear in J. Geom. Phy
Radiometric analysis of biological oxidations in man: sex differences in estradiol metabolism.
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