An obstruction to finding algebraic models for smooth manifolds with prescribed algebraic submanifolds

2001-03-01
CELIKTEN, A
Ozan, Yıldıray
Let N ⊆ M be a pair of closed smooth manifolds and L an algebraic model for the submanifold N. In this paper, we will give an obstruction to finding an algebraic model X of M so that the submanifold N corresponds in X to an algebraic subvariety isomorphic to L.
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY

Suggestions

Relative topology of real algebraic varieties in their complexifications
Ozan, Yıldıray (Mathematical Sciences Publishers, 2004-12-01)
We investigate, for a given smooth closed manifold M, the existence of an algebraic model X for M (i.e., a nonsingular real algebraic variety diffeomorphic to M) such that some nonsingular projective complexification i:X-->X-C of X admits a retraction r:X-C-->X. If such an X exists, we show that M must be formal in the sense of Sullivan's minimal models, and that all rational Massey products on M are trivial.
On homology of real algebraic varieties
Ozan, Yıldıray (American Mathematical Society (AMS), 2001-01-01)
Let R be a commutative ring with unity and X an R-oriented compact nonsingular real algebraic variety of dimension n. If i : X --> X-C is any nonsingular complexification of X, then the kernel, which we will denote by KHk(X, R), of the induced homomorphism i(*) : H-k(X, R) --> H-k(X-C, R) is independent of the complexification. In this work, we study KHk(X, R) and give some of its applications.
The Fine Moduli Space of Representations of Clifford Algebras
Coşkun, Emre (Oxford University Press (OUP), 2011-01-01)
Given a fixed binary form f(u,v) of degree d over a field k, the associated Clifford algebra is the k-algebra C(f)=k{u,v}/I, where I is the two-sided ideal generated by elements of the form (alpha u+beta v)(d)-f(alpha,beta) with alpha and beta arbitrary elements in k. All representations of C(f) have dimensions that are multiples of d, and occur in families. In this article, we construct fine moduli spaces U=U(f,r) for the irreducible rd-dimensional representations of C(f) for each r >= 2. Our construction ...
Invariant subspaces for Banach space operators with an annular spectral set
Yavuz, Onur (2008-01-01)
Consider an annulus Omega = {z epsilon C : r(0) 0 such that parallel to p(T)parallel to <= K sup{vertical bar p(lambda)vertical bar : vertical bar lambda vertical bar <= 1} and parallel to p(r(0)T(-1))parallel to <= K sup{vertical bar p(lambda)vertical bar : vertical bar lambda vertical bar <= 1} for all polynomials p. Then there exists a nontrivial common invariant subspace for T* and T*(-1).
An abstract approach to Bohr's phenomenon
Aizenberg, L; Aytuna, A; Djakov, P (American Mathematical Society (AMS), 2000-01-01)
In 1914 Bohr discovered that there exists r is an element of (0, 1) such that if a power series converges in the unit disk and its sum has modulus less than 1, then for \z\ < r the sum of absolute values of its terms is again less than 1. Recently analogous results were obtained for functions of several variables. Our aim here is to present an abstract approach to the problem and show that Bohr's phenomenon occurs under very general conditions.
Citation Formats
A. CELIKTEN and Y. Ozan, “An obstruction to finding algebraic models for smooth manifolds with prescribed algebraic submanifolds,” MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, pp. 281–286, 2001, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/49144.