MULTIPLICATIVE PARAMETRIZED HOMOTOPY THEORY VIA SYMMETRIC SPECTRA IN RETRACTIVE SPACES

被引：4

作者：

Hebestreit, Fabian ^{[1
]}

Sagave, Steffen ^{[2
]}

Schlichtkrull, Christian ^{[3
]}

机构：

[1] Univ Bonn, Math Inst, Endenicher Allee 60, D-53115 Bonn, Germany

[2] Radboud Univ Nijmegen, IMAPP, POB 9010, NL-6500 GL Nijmegen, Netherlands

[3] Univ Bergen, Dept Math, POB 7803, N-5020 Bergen, Norway

来源：

FORUM OF MATHEMATICS SIGMA | 2020年 / 8卷

基金：

英国工程与自然科学研究理事会;

关键词：

THOM SPECTRA; MODEL CATEGORIES; UNITS;

D O I：

10.1017/fms.2020.11

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In order to treat multiplicative phenomena in twisted (co)homology, we introduce a new point-set-level framework for parametrized homotopy theory. We provide a convolution smash product that descends to the corresponding $\infty$-categorical product and allows for convenient constructions of commutative parametrized ring spectra. As an immediate application, we compare various models for generalized Thom spectra. In a companion paper, this approach is used to compare homotopical and operator algebraic models for twisted K-theory.

引用

页数：84

共 50 条

[1] THE HOMOTOPY CATEGORY OF PARAMETRIZED SPECTRA
CLAPP, M
PUPPE, D
MANUSCRIPTA MATHEMATICA, 1984, 45 (03) : 219 - 247
[2] Semistable symmetric spectra in A1-homotopy theory
Haehne, Stephan
Hornbostel, Jens
NEW YORK JOURNAL OF MATHEMATICS, 2015, 21 : 1 - 56
[3] Homotopy theory of modules over operads in symmetric spectra
Harper, John E.
ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2009, 9 (03): : 1637 - 1680
[4] Parametrized Homotopy Theory and Fundamental Groupoids
Costenoble, Steven R.
Waner, Stefan
EQUIVARIANT ORDINARY HOMOLOGY AND COHOMOLOGY, 2016, 2178 : 155 - 202
[5] Parametrized spectra, multiplicative Thom spectra and the twisted Umkehr map
Ando, Matthew
Blumberg, Andrew J.
Gepner, David
GEOMETRY & TOPOLOGY, 2018, 22 (07) : 3761 - 3825
[6] Symmetric spectra model global homotopy theory of finite groups
Hausmann, Markus
ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2019, 19 (03): : 1413 - 1452
[7] Homotopy commutativity in symmetric spaces
Kishimoto, Daisuke
Minowa, Yuki
Miyauchi, Toshiyuki
Tong, Yichen
BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2024, 30 (02):
[8] Parametrized spaces model locally constant homotopy sheaves
Shulman, Michael A.
TOPOLOGY AND ITS APPLICATIONS, 2008, 155 (05) : 412 - 432
[9] On the homotopy groups of symmetric spectra
Schwede, Stefan
GEOMETRY & TOPOLOGY, 2008, 12 : 1313 - 1344
[10] Gauge Enhancement of Super M-Branes Via Parametrized Stable Homotopy Theory
Vincent Braunack-Mayer
Hisham Sati
Urs Schreiber
Communications in Mathematical Physics, 2019, 371 : 197 - 265

← 1 2 3 4 5 →