TL;DR
This paper investigates homological invariants of smooth real quadratic form families to develop a topological understanding of smooth maps via scalar Lagrange functions, aiming to extend Lagrange multipliers concepts.
Contribution
It introduces a new approach to analyze the topology of smooth maps using quadratic cohomology, advancing the theoretical framework for Lagrange multipliers in large-scale settings.
Findings
Development of quadratic cohomology theory
Application to topology of smooth maps
Foundations for Lagrange multipliers in large-scale analysis
Abstract
We study homological invariants of smooth families of real quadratic forms as a step towards a "Lagrange multipliers rule in the large" that intends to describe topology of smooth maps in terms of scalar Lagrange functions.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometry and complex manifolds · Algebraic Geometry and Number Theory