Massey Products and Critical Points
نویسنده
چکیده
In this paper we use cup-products and higher Massey products to find topological lower bounds on the minimal number of geometrically distinct critical points of any closed 1-form in a given cohomology class.
منابع مشابه
0 N ov 1 99 8 TOPOLOGY OF CLOSED 1 - FORMS AND THEIR CRITICAL POINTS
In this paper we suggest an analog of the Lusternik Schnirelman theory for closed 1-forms. Namely, we use cup-products and higher Massey products to find topological lower bounds on the minimal number of geometrically distinct critical points of any closed 1-form in a given cohomology class.
متن کاملMassey Products and Deformations
It is common knowledge that the construction of one-parameter deformations of various algebraic structures, like associative algebras or Lie algebras, involves certain conditions on cohomology classes, and that these conditions are usually expressed in terms of Massey products, or rather Massey powers. The cohomology classes considered are those of certain differential graded Lie algebras (DGLA...
متن کاملTriple Massey Products on Curves, Fay’s Trisecant Identity and Tangents to the Canonical Embedding
We show that Fay’s trisecant identity follows from the A∞-constraint satisfied by certain triple Massey products in the derived category of coherent sheaves on a curve. We also deduce the matrix analogue of this identity that can be conveniently formulated using quasideterminants of matrices with non-commuting entries. On the other hand, looking at more special Massey products we derive a formu...
متن کاملMatrix Factorizations, Minimal Models and Massey Products
We present a method to compute the full non–linear deformations of matrix factorizations for ADE minimal models. This method is based on the calculation of higher products in the cohomology, called Massey products. The algorithm yields a polynomial ring whose vanishing relations encode the obstructions of the deformations of the D–branes characterized by these matrix factorizations. This coinci...
متن کاملCritical Points of Functions on Singular Spaces
We compare and contrast various notions of the “critical locus” of a complex analytic function on a singular space. After choosing a topological variant as our primary notion of the critical locus, we justify our choice by generalizing Lê and Saito’s result that constant Milnor number implies that Thom’s af condition is satisfied.
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 2008