Homotopical Intersection Theory, Ii: Equivariance
نویسندگان
چکیده
This paper is a sequel to [KW]. We develop here an intersection theory for manifolds equipped with an action of a finite group. As in [KW], our approach will be homotopy theoretic, enabling us to circumvent the specter of equivariant transversality. We give applications of our theory to embedding problems, equivariant fixed point problems and the study of periodic points of self maps.
منابع مشابه
Homotopical intersection theory I
We give a new approach to intersection theory. Our “cycles” are closed manifolds mapping into compact manifolds and our “intersections” are elements of a homotopy group of a certain Thom space. The results are then applied in various contexts, including fixed point, linking and disjunction problems. Our main theorems resemble those of Hatcher and Quinn [H-Q], but our proofs are fundamentally di...
متن کاملOn Homological and Homotopical Algebra of Supersymmetries and Integrability in String Theory
The text contains introduction and preliminary definitions and results to my talk on category theory description of supersymmetries and integrability in string theory. In the talk I plan to present homological and homotopical algebra framework for Calabi-Yau supermanifolds and stacks in open and closed string theory. In the framework we investigate supersymmetries and integrability.
متن کاملBordism of Semi-free S 1-actions
We calculate the geometric and homotopical (or stable) bordism rings associated to semi-free S 1 actions on complex manifolds, giving explicit generators for the geometric theory. To calculate the geometric theory, we prove a case of the geometric realization conjecture, which in general would determine the geometric theory in terms of the homotopical. The determination of semi-free actions wit...
متن کاملEquivariance, Variational Principles, and the Feynman Integral
We argue that the variational calculus leading to Euler’s equations and Noether’s theorem can be replaced by equivariance and invariance conditions avoiding the action integral. We also speculate about the origin of Lagrangian theories in physics and their connection to Feynman’s integral.
متن کاملHomotopical Methods for Theoretical Computer Science
The purpose of this paper is to collect the homotopical methods used in the development of the theory of flows initialized by author’s paper “A model category for the homotopy theory of concurrency”. It is presented generalizations of the classical Whitehead theorem inverting weak homotopy equivalences between CW-complexes using weak factorization systems. It is also presented methods of calcul...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009