The Cobordism Hypothesis

Undergraduate Thesis of my MAJOR IN MATHEMATICS Department of Algebra and Geometry University of Barcelona Topological Quantum Field Theories: Towards The Cobordism Hypothesis

h-cobordism and s-cobordism Theorems: Transfer over Semialgebraic and Nash Categories, Uniform bound and Effectiveness

The h-cobordism theorem is a noted theorem in differential and PL topology. A generalization of the h-cobordism theorem for possibly non simply connected manifolds is the so called s-cobordism theorem. In this paper, we prove semialgebraic and Nash versions of these theorems. That is, starting with semialgebraic or Nash cobordism data, we get a semialgebraic homeomorphism (respectively a Nash d...

Complex cobordism of Hilbert manifolds

Slide 2 We will define a notion of cobordism generalizing that of Quillen: • D. G. Quillen, Elementary proofs of some results of cobordism theory using Steenrod operations, Adv. in Math. 7 (1971), 29–56. Details appear in • C. Özel, On the Complex Cobordism of Flag Varieties Associated to Loop Groups, PhD thesis, University of Glasgow (1998). • A. Baker & C. Özel, Complex cobordism of Hilbert m...

Fold Maps and Immersions from the Viewpoint of Cobordism

We obtain complete geometric invariants of cobordism classes of oriented simple fold maps of (n+ 1)-dimensional manifolds into an n-dimensional manifold N in terms of immersions with prescribed normal bundles. We compute that for N = R the cobordism group of simple fold maps is isomorphic to the direct sum of the (n−1)th stable homotopy group of spheres and the (n − 1)th stable homotopy group o...

Cobordism of Knots on Surfaces

We introduce a relation of cobordism for knots in thickened surfaces and study cobordism invariants of such knots. AMS Classification 57M27