An extension of Casson's invariant by Kevin Walker

By Kevin Walker

This publication describes an invariant, l, of orientated rational homology 3-spheres that's a generalization of labor of Andrew Casson within the integer homology sphere case. enable R(X) denote the gap of conjugacy sessions of representations of p(X) into SU(2). permit (W, W, F) be a Heegaard splitting of a rational homology sphere M. Then l(M) is said to be an adequately outlined intersection variety of R(W) and R(W) inside of R(F). The definition of this intersection quantity is a fragile job, because the areas concerned have singularities. A formulation describing how l transforms below Dehn surgical procedure is proved. The formulation contains Alexander polynomials and Dedekind sums, and will be used to offer a slightly straightforward facts of the lifestyles of l. it's also proven that once M is a Z-homology sphere, l(M) determines the Rochlin invariant of M

Show description

Read or Download An extension of Casson's invariant PDF

Similar topology books

Best Approximation in Inner Product Spaces

This ebook advanced from notes initially built for a graduate direction, "Best Approximation in Normed Linear Spaces," that i started giving at Penn country Uni­ versity greater than 25 years in the past. It quickly grew to become obtrusive. that the various scholars who desired to take the direction (including engineers, computing device scientists, and statis­ ticians, in addition to mathematicians) didn't have the mandatory necessities equivalent to a operating wisdom of Lp-spaces and a few uncomplicated practical research.

Topological automorphic forms

The authors observe a theorem of J. Lurie to provide cohomology theories linked to definite Shimura forms of kind $U(1,n-1)$. those cohomology theories of topological automorphic varieties ($\mathit{TAF}$) are regarding Shimura types within the similar manner that $\mathit{TMF}$ is said to the moduli area of elliptic curves.

Topological Methods, Variational Methods and Their Applications - Proceedings of the Icm2002 Satellite Conference on Nonlinear Functional Analysis

ICM 2002 satellite tv for pc convention on Nonlinear research used to be held within the interval: August 14-18, 2002 at Taiyuan, Shanxi Province, China. This convention was once equipped by way of Mathematical tuition of Peking college, Academy of arithmetic and approach Sciences of chinese language Academy of Sciences, Mathematical institution of Nankai college, and division of arithmetic of Shanxi collage, and used to be subsidized by means of Shanxi Province schooling Committee, Tian Yuan arithmetic origin, and Shanxi collage.

Additional resources for An extension of Casson's invariant

Example text

1. Let (Ω, A, P ) be a probability space, (V, · ) be a normed space and S a linear space of V -valued random variables (possibly the entire space). 1) where P is a probability measure on Ω. The couple (S, ν) is called an E-normed space (EN space). Such spaces have been introduced by Sherwood (1969, 1979). The results that follow have been established in Lafuerza-Guill´en, Rodr´ıguez Lallena and Sempi (1977) and Lafuerza-Guill´en and Sempi (2003). For the sake of completeness the complete proof will be reproduced adapting it from Sherwood (1969, 1979) although the new part, which is necessary in order to extend the proof to PN spaces, is that regarding axiom (N4).

It is therefore no surprise that many results, mainly in the area of fixed points, that hold in ordinary metric or normed spaces extend at once to Menger spaces under M . 7 Open Questions (1) Let (S, G) be an EN space with base (Ω, A, P ) and target (V, ·, · ). Then for every ω ∈ Ω, the function iω : S × S → R defined by iω p, q := p(ω), q(ω) is a pseudo-inner product on S. Since distinct functions p and q may agree at a particular point ω ∈ Ω, so that p(ω) = q(ω) while p = q, iω need not be an inner product on S.

An EN space (S, ν) is a PPN space under the triangle functions τW and τM . Proof. Only the proof of the properties (N3) and (N4) is needed. For all p, q, and r in S and for every t > 0, let u and v in [0, +∞] be such that page 38 June 30, 2014 17:11 Probabilistic Normed Spaces 9in x 6in b1779-ch02 39 Probabilistic Normed Spaces u + v = t. Define the sets A, B, and C by A = {ω ∈ Ω : p(ω) < u} B = {ω ∈ Ω : q(ω) < u} C = {ω ∈ Ω : p(ω) + q(ω) < u}. Since the norm · A ∩ B ⊂ C, so that satisfies the triangle inequality, it follows that P (C) ≥ P (A ∩ B) ≥ W (P (A), P (B)).

Download PDF sample

Rated 4.25 of 5 – based on 31 votes
 

Author: admin