Generalized Euler classes, differential forms and commutative DGAs

Alexander Gorokhovsky; Dennis Sullivan; Zhizhang Xie

doi:10.1142/S1793525319500043

Generalized Euler classes, differential forms and commutative DGAs

Alexander Gorokhovsky
, Dennis Sullivan
, Zhizhang Xie

Mathematics

University of Colorado Boulder
Texas A&M University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In the context of commutative differential graded algebras over as, we show that an iteration of "odd spherical fibration" creates a "total space" commutative differential graded algebra with only odd degree cohomology. Then we show for such a commutative differential graded algebra that, for any of its "fibrations" with "fiber" of finite cohomological dimension, the induced map on cohomology is injective.

Original language	English
Pages (from-to)	109-118
Number of pages	10
Journal	Journal of Topology and Analysis
Volume	11
Issue number	1
DOIs	https://doi.org/10.1142/S1793525319500043
State	Published - Mar 1 2019

Keywords

Euler class
fibrations with compact fibers
rational or DGA homotopy theory

Access to Document

10.1142/S1793525319500043

Cite this

@article{ad6b9b3db0d141a6bfae57ed06c0dc68,

title = "Generalized Euler classes, differential forms and commutative DGAs",

abstract = "In the context of commutative differential graded algebras over as, we show that an iteration of {"}odd spherical fibration{"} creates a {"}total space{"} commutative differential graded algebra with only odd degree cohomology. Then we show for such a commutative differential graded algebra that, for any of its {"}fibrations{"} with {"}fiber{"} of finite cohomological dimension, the induced map on cohomology is injective.",

keywords = "Euler class, fibrations with compact fibers, rational or DGA homotopy theory",

author = "Alexander Gorokhovsky and Dennis Sullivan and Zhizhang Xie",

note = "Publisher Copyright: {\textcopyright} 2019 World Scientific Publishing Company.",

year = "2019",

month = mar,

day = "1",

doi = "10.1142/S1793525319500043",

language = "English",

volume = "11",

pages = "109--118",

journal = "Journal of Topology and Analysis",

issn = "1793-5253",

number = "1",

}

TY - JOUR

T1 - Generalized Euler classes, differential forms and commutative DGAs

AU - Gorokhovsky, Alexander

AU - Sullivan, Dennis

AU - Xie, Zhizhang

PY - 2019/3/1

Y1 - 2019/3/1

N2 - In the context of commutative differential graded algebras over as, we show that an iteration of "odd spherical fibration" creates a "total space" commutative differential graded algebra with only odd degree cohomology. Then we show for such a commutative differential graded algebra that, for any of its "fibrations" with "fiber" of finite cohomological dimension, the induced map on cohomology is injective.

AB - In the context of commutative differential graded algebras over as, we show that an iteration of "odd spherical fibration" creates a "total space" commutative differential graded algebra with only odd degree cohomology. Then we show for such a commutative differential graded algebra that, for any of its "fibrations" with "fiber" of finite cohomological dimension, the induced map on cohomology is injective.

KW - Euler class

KW - fibrations with compact fibers

KW - rational or DGA homotopy theory

UR - https://www.scopus.com/pages/publications/85023196569

U2 - 10.1142/S1793525319500043

DO - 10.1142/S1793525319500043

M3 - Article

AN - SCOPUS:85023196569

SN - 1793-5253

VL - 11

SP - 109

EP - 118

JO - Journal of Topology and Analysis

JF - Journal of Topology and Analysis

IS - 1

ER -

Generalized Euler classes, differential forms and commutative DGAs

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this