3-manifold Groups and Nonpositive Curvature by Kapovich M.

By Kapovich M.

Show description

Read or Download 3-manifold Groups and Nonpositive Curvature PDF

Best differential geometry books

Minimal surfaces and Teichmuller theory

The notes from a suite of lectures writer brought at nationwide Tsing-Hua college in Hsinchu, Taiwan, within the spring of 1992. This notes is the a part of e-book "Thing Hua Lectures on Geometry and Analisys".

Complex, contact and symmetric manifolds: In honor of L. Vanhecke

This booklet is targeted at the interrelations among the curvature and the geometry of Riemannian manifolds. It comprises study and survey articles in line with the most talks brought on the foreign Congress

Differential Geometry and the Calculus of Variations

During this ebook, we learn theoretical and useful elements of computing tools for mathematical modelling of nonlinear structures. a couple of computing thoughts are thought of, similar to tools of operator approximation with any given accuracy; operator interpolation ideas together with a non-Lagrange interpolation; equipment of approach illustration topic to constraints linked to innovations of causality, reminiscence and stationarity; equipment of method illustration with an accuracy that's the most sensible inside a given category of versions; tools of covariance matrix estimation;methods for low-rank matrix approximations; hybrid equipment in response to a mix of iterative approaches and most sensible operator approximation; andmethods for info compression and filtering lower than situation filter out version may still fulfill regulations linked to causality and forms of reminiscence.

Extra info for 3-manifold Groups and Nonpositive Curvature

Example text

32 (and keeping the same notation), U ◦ j = Id. 61). 19) for a Dirac realization, it follows that i is injective. By a dimension argument, it follows that the sequence is exact. We now concentrate on constructing the quasi-Poisson bivector field π . 20, we have the following. 35. π is well defined. Proof. 29). Hence it must be in the image of i. More explicitly, we find that there exists an X such that ∗ (X, C ∗ (α)) ∈ L, ρ ∨ (dJ (X) + (σ ∨ )∗ ρM (α)) = 0. 31) to replace CρM , we find that ∗ σ ∗ (dJ (X) + (σ ∨ )∗ ρM (α)) = 0.

Since (iii) and the Leibniz identity for [·, ·] are together equivalent to (iv), it follows that (i)–(iv) are equivalent to each other. 7. If (M, π ) is a quasi-Poisson g-manifold, then the generalized distribution π (α) + ρM (v) ⊆ T M, for α ∈ T ∗ M, v ∈ g, is integrable. This result shows that the singular distribution discussed in [2, Thm. 2] in the context of Hamiltonian quasi-Poisson manifolds is integrable even without the presence of a moment map (and without the positivity of (·, ·)g ).

There is a one-to-one correspondence between presymplectic realizations of G endowed with the Cartan–Dirac structure, and quasi-Hamiltonian gmanifolds. 15, we conclude that general Dirac realizations of Cartan–Dirac structures must be “foliated’’ by quasi-Hamiltonian gmanifolds. Since Hamiltonian quasi-Poisson manifolds, in the sense of [2], also have this property [2, Sec. 10], we are led to investigate the relationship between these objects. 1 The equivalence theorem For a quasi-Poisson g-manifold (M, π), a momentum map is a g-equivariant map J : M −→ G (with respect to the infinitesimal action by conjugation on G) satisfying the condition [2, Lem.

Download PDF sample

Rated 4.22 of 5 – based on 19 votes