39 citations · 41 across the 15 of their papers we have counts for
15 papers
Computing Topological Invariants Using Fixed Points
Loring W. Tu
When a torus acts on a compact oriented manifold with isolated fixed points, the equivariant localization formula of Atiyah--Bott and Berline--Vergne converts the integral of an eq…
Equivariant Characteristic Classes
Loring W. Tu
This is a commentary on Raoul Bott and Loring Tu's joint article "Equivariant characteristic classes in the Cartan model," which appeared in "Geometry, Analysis, and Applications (…
Gysin formulas and equivariant cohomology
Loring W. Tu
Under Poincaré duality, a smooth map of compact oriented manifolds induces a pushforward map in cohomology, called the "Gysin map." It plays an important role in enumerative geomet…
Lefschetz fixed point theorems for correspondences
Loring W. Tu
The classical Lefschetz fixed point theorem states that the number of fixed points, counted with multiplicity , of a smooth map from a manifold to itself can be calc…
Introduction to Sheaf Cohomology
Loring W. Tu
This article aims to introduce to the uninitiated, in just four lectures of 26 pages, the wonderful techniques of sheaf cohomology, hypercohomology, and spectral sequences.
Basis-Free Analysis of Singular Tuples and Eigenpairs of Tensors
Joao Marcos Vensi Basso, Loring W. Tu
A tensor in applied mathematics is usually defined as a multidimensional array of numbers. This presumes a choice of basis in or in some other vector space, and tens…