However, the gauge theory invariants run into trouble with small 4-manifolds, such as those with the same homology groups as the 4D sphere, S 4. In particular, the smooth 4D Poincaré Conjecture, the ...

Transactions of the American Mathematical Society, Vol. 276, No. 2 (Apr., 1983), pp. 625-643 (19 pages) In this paper we prove that every smooth paracompact connected ...

The course gives an introduction to smooth manifolds. It covers tangent bundles, vector fields and integral curves (ordinary differential equations), Lie groups, differential forms, and integration.

This is an attempt at an intuitive, bottom-up approach to modern differential geometry, covering deep topics in maximum detail with minimal prerequisites. Too often in math education, fundamental ...

We give a short historical review of early Kaluza-Klein theories. We study various causal structures on manifolds, especially those which cannot be described by a metric tensor with signature (+---).

In this paper, we use homotopical algebra (or abstract homotopical methods) to study smooth homotopical problems of infinite-dimensional \(C^\infty\)-manifolds in convenient calculus. More precisely, ...

This is an attempt at a bottom-up approach to modern differential geometry, covering deep topics in maximum detail with minimal prerequisites. Too often in math education, fundamental concepts are ...

Abstract: Estimation algebras have been extensively studied in Euclidean space, where finite-dimensional estimation algebras form the foundation of the Kalman and Benes filters, and have contributed ...

The Math 8806-8807 sequence will cover the following topics: Group Theory (Group actions, Sylow, Nilpotent/Solvable, simple groups, Jordan-Holder series, presentations); commutative algebra ...