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The cobordism category and Waldhausen's K-theory

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The cobordism category and Waldhausen's K-theory. / Bökstedt, M.; Madsen, Ib.

arXiv.org, 2011.

Publikation: Working paperForskning

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@techreport{bbbb99860ca144bc965d555ddb9d5aa4,
title = "The cobordism category and Waldhausen's K-theory",
abstract = "This paper examines the category C^k_{d,n} whose morphisms are d-dimensional smooth manifolds that are properly embedded in the product of a k-dimensional cube with an (d+n-k)-dimensional Euclidean space. There are k directions to compose k-dimensional cubes, so C^k_{d,n} is a (strict) k-tuple category. The geometric realization of the k-dimensional multi-nerve is the classifying space BC^k_{d,n}. At the end of the paper we construct an infinite loop map to Waldhausens K-theory. \Omega BC^1_{d,n}-> A(BO(d)), We believe that the map factors through \Omega^\infty\Sigma^\infty(BO(d)_+) and that the composite B{Diff}(M^d)\to A(BO(d)) is homotopic to the map considered by Dwyer, Williams and Weiss.",
keywords = "math.AT, math.GT",
author = "M. B{\"o}kstedt and Ib Madsen",
year = "2011",
month = feb,
day = "21",
language = "English",
publisher = "arXiv.org",
type = "WorkingPaper",
institution = "arXiv.org",

}

RIS

TY - UNPB

T1 - The cobordism category and Waldhausen's K-theory

AU - Bökstedt, M.

AU - Madsen, Ib

PY - 2011/2/21

Y1 - 2011/2/21

N2 - This paper examines the category C^k_{d,n} whose morphisms are d-dimensional smooth manifolds that are properly embedded in the product of a k-dimensional cube with an (d+n-k)-dimensional Euclidean space. There are k directions to compose k-dimensional cubes, so C^k_{d,n} is a (strict) k-tuple category. The geometric realization of the k-dimensional multi-nerve is the classifying space BC^k_{d,n}. At the end of the paper we construct an infinite loop map to Waldhausens K-theory. \Omega BC^1_{d,n}-> A(BO(d)), We believe that the map factors through \Omega^\infty\Sigma^\infty(BO(d)_+) and that the composite B{Diff}(M^d)\to A(BO(d)) is homotopic to the map considered by Dwyer, Williams and Weiss.

AB - This paper examines the category C^k_{d,n} whose morphisms are d-dimensional smooth manifolds that are properly embedded in the product of a k-dimensional cube with an (d+n-k)-dimensional Euclidean space. There are k directions to compose k-dimensional cubes, so C^k_{d,n} is a (strict) k-tuple category. The geometric realization of the k-dimensional multi-nerve is the classifying space BC^k_{d,n}. At the end of the paper we construct an infinite loop map to Waldhausens K-theory. \Omega BC^1_{d,n}-> A(BO(d)), We believe that the map factors through \Omega^\infty\Sigma^\infty(BO(d)_+) and that the composite B{Diff}(M^d)\to A(BO(d)) is homotopic to the map considered by Dwyer, Williams and Weiss.

KW - math.AT

KW - math.GT

M3 - Working paper

BT - The cobordism category and Waldhausen's K-theory

PB - arXiv.org

ER -