Automorphisms of Surfaces after Nielsen and Thurston by Andrew J. Casson

By Andrew J. Casson

This booklet, which grew out of Steven Bleiler's lecture notes from a direction given through Andrew Casson on the collage of Texas, is designed to function an creation to the purposes of hyperbolic geometry to low dimensional topology. particularly it offers a concise exposition of the paintings of Neilsen and Thurston at the automorphisms of surfaces. The reader calls for in basic terms an realizing of simple topology and linear algebra, whereas the early chapters on hyperbolic geometry and geometric buildings on surfaces can profitably be learn through a person with a data of normal Euclidean geometry aspiring to examine extra abour different 'geometric structures'.

Show description

Read Online or Download Automorphisms of Surfaces after Nielsen and Thurston PDF

Best topology books

Modern Geometry: Introduction to Homology Theory Pt. 3: Methods and Applications

Over the last fifteen years, the geometrical and topological tools of the idea of manifolds have assumed a imperative function within the so much complex parts of natural and utilized arithmetic in addition to theoretical physics. the 3 volumes of "Modern Geometry - tools and functions" include a concrete exposition of those equipment including their major purposes in arithmetic and physics.

Borel Liftings of Borel Sets: Some Decidable and Undecidable Statements

One of many goals of this paintings is to enquire a few usual houses of Borel units that are undecidable in $ZFC$. The authors' place to begin is the subsequent ordinary, although non-trivial end result: contemplate $X \subset 2omega\times2omega$, set $Y=\pi(X)$, the place $\pi$ denotes the canonical projection of $2omega\times2omega$ onto the 1st issue, and feel that $(\star)$ : ""Any compact subset of $Y$ is the projection of a few compact subset of $X$"".

Extra resources for Automorphisms of Surfaces after Nielsen and Thurston

Sample text

Likewise, as there are two independent twisted supersymmetries, and the D-brane generically preserves 1/2 of the supersymmetries left unbroken by the compactification, we need a 7 manifold preserving 1/8-th of the supersymmetry. This is a 7-manifold of G2 holonomy, which indeed has supersymmetric 4-cycles whose normal bundle is precisely Ω2,+ (X) (the bundle of self-dual two-forms on X), as expected. A similar analysis [9] shows that the second twist arises in compactifications on an 8-dimensional Spin(7)-holonomy manifold, while the amphicheiral theory is realized on supersymmetric cycles of SU(4)-holonomy Calabi-Yau 4-folds.

Instead of writing the full expression for the Mathai-Quillen form, we define the action to be {Q, Ψ} for some appropriate gauge invariant gauge fermion Ψ [20]. The use of gauge fermions was introduced in the context of topological quantum field theory in [68] (see [10] for a review). 31) in T M and Ω0 (X, adP ). 41) ˜ ∈ T(A,C,B+ ) M. 40) the expression: where (ψ, ζ, ψ) √ Ψproj = X i + g Tr φ¯ −Dµ ψ µ + [ψ˜µν , B +µν ] + i[ζ, C] 2 . 42). However, as in the case of the Mathai-Quillen formulation of Donaldson-Witten theory [6], one must add another piece to the gauge fermion to make full contact with the corresponding twisted supersymmetric theory.

Now, the Montonen-Olive duality conjecture [83] follows simply as the statement that the electric and magnetic factors are exchanged under an inversion of the coupling constant e0 → 1/e0 . Let us consider the example H = SU(N) in detail. Since SU(N) is simply laced, SU(N) and SU(N)v have the same Lie algebra su(N). Also, we can identify the coweight SU (N ) SU (N ) SU (N )v = lattice of SU(N) with the root lattice of su(N). Thus, Λweight = Λcoweight = Λroot v v v SU (N ) SU (N ) SU (N ) H v H , SU(N) has no center (Λweight /Λroot ≃ Center(H)), .

Download PDF sample

Rated 4.65 of 5 – based on 31 votes