New directions in homotopy theory : Second Mid-Atlantic Topology Conference, March 12-13, 2016, Johns Hopkins University, Baltimore, Maryland / Nitya Kitchloo [and four others].

Format:

Book

Conference/Event

Contributor:

Kitchloo, Nitya, editor.

Conference Name:

Mid-Atlantic Topology Conference (2nd : 2016 : Baltimore, Md.)

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 707

Contemporary mathematics, 707 0271-4132

Language:

English

Subjects (All):

Homotopy theory--Congresses.

Homotopy theory.

Topology--Congresses.

Topology.

Physical Description:

1 online resource (208 pages).

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2018]

Summary:

This volume contains the proceedings of the Second Mid-Atlantic Topology Conference, held from March 12-13, 2016, at Johns Hopkins University in Baltimore, Maryland. The focus of the conference, and subsequent papers, was on applications of innovative methods from homotopy theory in category theory, algebraic geometry, and related areas, emphasizing the work of younger researchers in these fields.

Contents:

Cover

Title page

Contents

Preface

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Hy @SectionAnchorHref {conm14249.section*.5}Sectionformat {Acknowledgements }{@m }

The stable Galois correspondence for real closed fields

1. Introduction

2. Preliminaries

3. Comparing stable stems

4. Proof of Theorem 1.1

References

An Étale realization which does NOT exist

2. Enriched Euler characteristics and genuine \Gal_{\bbb{ }}-realization

3. Enriched Euler characteristics and restrictions on genuine \Gal_{ }-realization

Acknowledgements

Multiplicative structure on Real Johnson-Wilson theory

2. Background

3. A stable multiplicative structure

4. Multiplicative structure on \MU₍₂₎[ _{ }⁻¹]

5. Unstable properties of the multiplicative structure

6. The MR( ) orientation for MO[2ⁿ⁺¹] revisited

The Morita equivalence between parametrized spectra and module spectra

2. Cell complexes and parametrized homotopy theory

3. \cC-spectra and spectra over \cC

4. The aggregate model structure

5. The case where \cC is a groupoid up to homotopy

6. Indexed symmetric monoidal categories

7. Costenoble-Waner dualizable spectra

tmf is not a ring spectrum quotient of string bordism

2. The Koszul Complex \K( )

3. _{*}( / ) is Rationally Isomorphic to _{*}(\Tot(\K( )))

4. _{*}( )→ _{*}( / ) is surjective only if is a quasi-regular sequence

5. The kernel of the -local Witten genus cannot be generated by a quasi-regular sequence

Acknowledgments

Cocycle schemes and [2 ,∞)-orientations.

1. Motivation: Integration in extraordinary cohomology theories

2. The algebraic geometry of the Thom construction

3. Orientations for and [6,∞)

4. Orientations for [2 ,∞)?

The linearity of fixed point invariants

Part 1. Topological fixed-point invariants

2. The Lefschetz number as a trace

3. Linearity of the Lefschetz number

4. Parametrized spaces and the Reidemeister trace

5. Parametrized profunctors

6. Linearity of the Reidemeister traces

Part 2. Indexed monoidal derivators

7. Background

8. Indexed monoidal derivators

9. Closed structures

10. Indexed monoidal model categories

Homotopy coherent centers versus centers of homotopy categories

Introduction

1. Categories enriched in spaces and their centers

2. Homotopy coherent centers

3. Multiplicative structure

4. Functoriality and equivalences

5. Monoids and groups

6. The homotopy limit problem

7. Spectral sequences and obstructions

8. Groupoids and spaces

Recent developments on noncommutative motives

1. Additive invariants

2. Noncommutative pure motives

3. Noncommutative (standard) conjectures

4. Noncommutative motivic Galois groups

5. Localizing invariants

6. Noncommutative mixed motives

7. Noncommutative realizations and periods

The category of Waldhausen categories is a closed multicategory

1. A quick introduction to symmetric multicategories

2. A bit about Waldhausen categories

3. Cubes

4. -exactness

5. The closed structure

6. -Theory as an enriched multifunctor

Appendix A. Proof of Lemma 3.4

Back Cover.

Notes:

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-4772-X