Riemann surfaces and spin structures
نویسندگان
چکیده
منابع مشابه
Spin Structures on Riemann Surfaces and the Perfect Numbers
The equality between the number of odd spin structures on a Riemann surface of genus g, with 2 g − 1 being a Mersenne prime, and the even perfect numbers suggests that properties of the set of spin structures might provide an indication of whether the sequence of perfect numbers continues indefinitely. A method for determining whether Mersenne numbers are primes is developed by using a geometri...
متن کاملRiemann Surfaces
Riemann introduced his surfaces in the middle of the 19th century in order to “geometrize” complex analysis. In doing so, he paved the way for a great deal of modern mathematics such as algebraic geometry, manifold theory, and topology. So this would certainly be of interest to students in these areas, as well as in complex analysis or number theory. In simple terms, a Riemann surface is a surf...
متن کاملThe Moduli of Flat Pu(2,1) Structures on Riemann Surfaces
For a compact Riemann surface X of genus g > 1, Hom(π1(X),PU(p, q))/PU(p, q) is the moduli space of flat PU(p, q)-connections on X. There are two integer invariants, dP , dQ, associated with each σ ∈ Hom(π1(X),PU(p, q))/ PU(p, q). These invariants are related to the Toledo invariant τ by τ = 2P −pdQ p+q . This paper shows, via the theory of Higgs bundles, that if q = 1, then −2(g − 1) ≤ τ ≤ 2(g...
متن کاملCrystallography and Riemann Surfaces
The level set of an elliptic function is a doubly periodic point set in C. To obtain a wider spectrum of point sets, we consider, more generally, a Riemann surface S immersed in C2 and its sections (“cuts”) by C. We give S a crystallographic isometry in C2 by defining a fundamental surface element as a conformal map of triangular domains and S as its extension by reflections in the triangle edg...
متن کاملRiemann Surfaces and Differential
We present a new approach to the diierential geometry of surfaces in R 3 and R 4 that treats this theory as a \quaternioniied" version of the complex analysis and algebraic geometry of Riemann surfaces.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales scientifiques de l'École normale supérieure
سال: 1971
ISSN: 0012-9593,1873-2151
DOI: 10.24033/asens.1205