Mapping spaces from a rational point of view

Slides:

Advertisements

Similar presentations

Section 13 Homomorphisms Definition A map  of a group G into a group G’ is a homomorphism if the homomophism property  (ab) =  (a)  (b) Holds for.

Advertisements

Chapter 5. Operations on Multiple R. V.'s 1 Chapter 5. Operations on Multiple Random Variables 0. Introduction 1. Expected Value of a Function of Random.

Fundamental Group

2.6 – Proving Statements about Angles Definition: Theorem A true statement that follows as a result of other true statements.

Sullivan Algebra and Trigonometry: Section 5.6 Complex Zeros; Fundamental Theorem of Algebra Objectives Utilize the Conjugate Pairs Theorem to Find the.

MAT 4725 Numerical Analysis Section 7.1 (Part II) Norms of Vectors and Matrices

Copyright © 2013 Pearson Education. All rights reserved. Chapter 1 Introduction to Statistics and Probability.

Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Chapter 2 Probability.

Positively Expansive Maps and Resolution of Singularities Wayne Lawton Department of Mathematics National University of Singapore

Introduction to Real Analysis Dr. Weihu Hong Clayton State University 10/7/2008.

CS Lecture 14 Powerful Tools     !. Build your toolbox of abstract structures and concepts. Know the capacities and limits of each tool.

EXAMPLE 1 List possible rational zeros List the possible rational zeros of f using the rational zero theorem. a. f (x) = x 3 + 2x 2 – 11x + 12 Factors.

Erik Jonsson School of Engineering and Computer Science FEARLESS Engineering ENGR 3300 – 505 Advanced Engineering Mathematics

MA5209 Algebraic Topology Wayne Lawton Department of Mathematics National University of Singapore S ,

Introduction to Real Analysis Dr. Weihu Hong Clayton State University 11/11/2008.

DEFINITION OF A GROUP A set of elements together with a binary operation that satisfies Associativity: Identity: Inverses:

Section 1.8 Continuity. CONTINUITY AT A NUMBER a.

Algebra 2. Solve for x Algebra 2 (KEEP IN MIND THAT A COMPLEX NUMBER CAN BE REAL IF THE IMAGINARY PART OF THE COMPLEX ROOT IS ZERO!) Lesson 6-6 The Fundamental.

String Lie bialgebra in manifolds

Algebraic Topology Simplicial Homology Wayne Lawton

Warm Up Compute the following by using long division.

MAT 3749 Introduction to Analysis

EOC Practice #13 SPI

Cyclic Codes 1. Definition Linear:

PHY 745 Group Theory 11-11:50 AM MWF Olin 102 Plan for Lecture 36:

Chapter 6 Section 3.

MTH 324 Lecture # 18 Complex Integration.

4.4 The Fundamental Theorem of Calculus

5.6 – Find the Rational Zeros

Automatically trivial fibrations

Introduction to the Concept of a Limit

Hire Toyota Innova in Delhi for Outstation Tour

Introduction to Measure Theory

Introduction to Functions

Linear Transformations

Chapter 7 Functions of Random Variables (Optional)

GROUPS & THEIR REPRESENTATIONS: a card shuffling approach

1-5 Postulates and Theorems Relating Points, Lines and Planes

Polar actions on complex hyperbolic spaces

Advanced Engineering Mathematics

Countable and Countably Infinite Sets

Sullivan Algebra and Trigonometry: Section 8.1

Homomorphisms (11/20) Definition. If G and G’ are groups, a function  from G to G’ is called a homomorphism if it is operation preserving, i.e., for all.

Rational and irrational subgrouping

Limits at Infinity and Limits of Sequences

5.7 Rational Exponents 1 Rules 2 Examples 3 Practice Problems.

Higher order Whitehead products in Quillen’s models

One-to-One and Onto, Inverse Functions

Introduction to Real Analysis

11.10 – Taylor and Maclaurin Series

Sullivan Algebra and Trigonometry: Section 6.1

Lecture 37 Section 7.2 Tue, Apr 3, 2007

Theorems about LINEAR MAPPINGS.

TOPOLOGICAL COMPLEXITY OF KINEMATIC MAPS

10th International Conference of University Teaching and Innovation

PHY 752 Solid State Physics

Limits and Continuity A BRIEF PREVIEW OF CALCULUS: TANGENT LINES AND THE LENGTH OF A CURVE 1.2 THE CONCEPT OF LIMIT 1.3 COMPUTATION OF LIMITS 1.4.

Limits and Continuity An introduction to Limits and how we will be using them.

TOPOLOGICAL COMPLEXITY OF FIBRATIONS AND COVERING MAPS

Notes Over 6.6 Possible Zeros Factors of the constant

Advanced Engineering Mathematics

8-5 Rational Zero Theorem

5.1 Integrals Rita Korsunsky.

Mean Value Theorem AP Calculus Ms. Olifer.

ENGR 3300 – 505 Advanced Engineering Mathematics

FIBRATIONS WITH UNIQUE PATH LIFTING PROPERTY

5.5 Further Properties of the Riemann Integral II

Trigonometry rules Sunday, 28 July 2019.

TAYLOR SERIES Maclaurin series ( center is 0 )

Presentation transcript:

Mapping spaces from a rational point of view 5/9/2019 Mapping spaces from a rational point of view (Joint work with Urtzi Buijs) Tokyo, July 2005

Kotani Kuribayashi Lupton Credits Bousfield Brown F.Cohen Félix Haefliger Kotani Kuribayashi Lupton Möller Peterson Rausen Shibata Shiga L.Smith S.Smith Sullivan Szczarba Tanré Taylor Thom Vigué Yamaguchi

A brief introduction

Definition Theorem (Brown-Szczarba)

A model for the evaluation fibration Problem Corollary Theorem Remark

The restriction to components

Corollary Theorem

The homotopy groups Theorem

Evaluation subgroups (Gottlieb groups) Corollary

More consequences… d It generalizes and complements previous work by Y. Félix, Y. Kotani, D. Tanré and M. Vigué