Leçons sur la théorie générale des surfaces by Darboux G.

By Darboux G.

Show description

Read or Download Leçons sur la théorie générale des surfaces PDF

Similar geometry and topology books

Differential Geometry. Proc. conf. Lyngby, 1985

The Nordic summer season university 1985 offered to younger researchers the mathematical points of the continuing examine stemming from the examine of box theories in physics and the differential geometry of fibre bundles in arithmetic. the quantity contains papers, frequently with unique strains of assault, on twistor tools for harmonic maps, the differential geometric features of Yang-Mills concept, complicated differential geometry, metric differential geometry and partial differential equations in differential geometry.

Geometric Aspects of Functional Analysis: Israel Seminar (GAFA) 1986–87

This can be the 3rd released quantity of the lawsuits of the Israel Seminar on Geometric points of useful research. the big majority of the papers during this quantity are unique learn papers. there has been final 12 months a powerful emphasis on classical finite-dimensional convexity idea and its reference to Banach area idea.

Lectures on the geometry of quantization

Those notes are according to a direction entitled "Symplectic Geometry and Geometric Quantization" taught by way of Alan Weinstein on the college of California, Berkeley (fall 1992) and on the Centre Emile Borel (spring 1994). the one prerequisite for the direction wanted is a data of the fundamental notions from the idea of differentiable manifolds (differential types, vector fields, transversality, and so on.

Additional resources for Leçons sur la théorie générale des surfaces

Example text

3. Theorem. Let G = (X / R) where R is cyclically reduced. (a) If R is not a proper power in the free group F(X), then G is torsion-free. 7. Theorem. Any soluble subgroup of a one-relator group G is either locally cyclic or metabelian of the form (a, b I aba-’ = bm). ,c~ ). By the inductive hypothesis the problems of membership in the subgroups (ba, bl , cj : j E Z) and : j E Z) are solvable and hence the word problem for G is solv(Wwj able. Of course more must be squeezed out to continue the induction but the normal form for HNN-extensions is sufficiently powerful to obtain the desired information.

The importance of this group in topology is unquestioned and Dehn’s solutions of the word and conjugacy problems can be regarded as the coming of age of combinatorial group theory. It was also Dehn who suggested that significant results generalising those for surface groups could be obtained for arbitrary groups given by a single defining relator. The theory begins with two classic results of Magnus [Magnus 1930, 19311. 18. Let o E Aut F and let H = Fix(a). Let X be the coset graph of H - then by the theory of coverings H ” rr(X).

Similar arguments apply except for the cases g = 0, m < 3; g = 1, m 5 1. For g = 1 = m we pass to a quotient group by introducing the relations uy, sit: and obtain the presentation (tl, u1 1 tThl, UT,t~lult~lu~l) of the dihedral group &hl of order 2h1 where it is trivial to check that no proper subword of a defining relation is a relation. For g = 0, m < 3 the groups with m 5 2 are excluded (the groups are finite cyclic groups). 12 to obtain s” # 1 if k$Omodhi. 11. We will not do this here, but will use geometric arguments instead.

Download PDF sample

Rated 4.55 of 5 – based on 31 votes