Embedded Cobordism Categories and Spaces of Submanifolds

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Embedded Cobordism Categories and Spaces of Submanifolds. / Randal-Williams, Oscar.

I: International Mathematics Research Notices, Bind 2011, Nr. 3, 2011, s. 572-608.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Randal-Williams, O 2011, 'Embedded Cobordism Categories and Spaces of Submanifolds', International Mathematics Research Notices, bind 2011, nr. 3, s. 572-608. https://doi.org/10.1093/imrn/rnq072

APA

Randal-Williams, O. (2011). Embedded Cobordism Categories and Spaces of Submanifolds. International Mathematics Research Notices, 2011(3), 572-608. https://doi.org/10.1093/imrn/rnq072

Vancouver

Randal-Williams O. Embedded Cobordism Categories and Spaces of Submanifolds. International Mathematics Research Notices. 2011;2011(3):572-608. https://doi.org/10.1093/imrn/rnq072

Author

Randal-Williams, Oscar. / Embedded Cobordism Categories and Spaces of Submanifolds. I: International Mathematics Research Notices. 2011 ; Bind 2011, Nr. 3. s. 572-608.

Bibtex

@article{9b703a30d7da11df825b000ea68e967b,
title = "Embedded Cobordism Categories and Spaces of Submanifolds",
abstract = "Galatius, Madsen, Tillmann, and Weiss [7] have identified the homotopy type of the classifying space of the cobordism category with objects (d -1)-dimensional manifolds embedded in R8. In this paper we apply the techniques of spaces of manifolds, as developed by the author and Galatius in [8], to identify the homotopy type of the cobordism category with objects (d -1)-dimensional submanifolds of a fixed background manifold M. There is a description in terms of a space of sections of a bundle over M associated to its tangent bundle. This can be interpreted as a form of Poincar{\'e} duality, relating a space of submanifolds of M to a space of functions on M. ",
author = "Oscar Randal-Williams",
year = "2011",
doi = "10.1093/imrn/rnq072",
language = "English",
volume = "2011",
pages = "572--608",
journal = "International Mathematics Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",
number = "3",

}

RIS

TY - JOUR

T1 - Embedded Cobordism Categories and Spaces of Submanifolds

AU - Randal-Williams, Oscar

PY - 2011

Y1 - 2011

N2 - Galatius, Madsen, Tillmann, and Weiss [7] have identified the homotopy type of the classifying space of the cobordism category with objects (d -1)-dimensional manifolds embedded in R8. In this paper we apply the techniques of spaces of manifolds, as developed by the author and Galatius in [8], to identify the homotopy type of the cobordism category with objects (d -1)-dimensional submanifolds of a fixed background manifold M. There is a description in terms of a space of sections of a bundle over M associated to its tangent bundle. This can be interpreted as a form of Poincaré duality, relating a space of submanifolds of M to a space of functions on M.

AB - Galatius, Madsen, Tillmann, and Weiss [7] have identified the homotopy type of the classifying space of the cobordism category with objects (d -1)-dimensional manifolds embedded in R8. In this paper we apply the techniques of spaces of manifolds, as developed by the author and Galatius in [8], to identify the homotopy type of the cobordism category with objects (d -1)-dimensional submanifolds of a fixed background manifold M. There is a description in terms of a space of sections of a bundle over M associated to its tangent bundle. This can be interpreted as a form of Poincaré duality, relating a space of submanifolds of M to a space of functions on M.

U2 - 10.1093/imrn/rnq072

DO - 10.1093/imrn/rnq072

M3 - Journal article

VL - 2011

SP - 572

EP - 608

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 3

ER -

ID: 22502971