publication . Preprint . 2013

Geometric homology revisited

Ruffino, Fabio Ferrari;
Open Access English
  • Published: 24 Jan 2013
Abstract
Given a cohomology theory, there is a well-known abstract way to define the dual homology theory using the theory of spectra. In [4] the author provides a more geometric construction of the homology theory, using a generalization of the bordism groups. Such a generalization involves in its definition the vector bundle modification, which is a particular case of the Gysin map. In this paper we provide a more natural variant of that construction, which replaces the vector bundle modification with the Gysin map itself, which is the natural push-forward in cohomology. We prove that the two constructions are equivalent.
Subjects
arXiv: Mathematics::Algebraic TopologyMathematics::K-Theory and Homology
free text keywords: Mathematics - Algebraic Topology, Mathematics - K-Theory and Homology
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[1] F. Ferrari Ruffino, Gysin map and Atiyah-Hirzebruch spectral sequence, Bollettino UMI (9) IV (2011), arXiv:0904.4103

[2] M. Hirsh, Differential topology, Springer-Verlag, 1994

[3] M. J. Hopkins and I. M. Singer, Quadratic functions in geometry, topology,and M-theory, J.Diff.Geom. 70 (2005) 329-452, arXiv:math/0211216

[4] A. Jakob, A bordism-type description of homology, manuscripta math. 96, 67-80 (1998)

[5] M. Karoubi, K-theory: an Introduction, Springer-Verlag, 1978

[6] A. A. Kosinski, Differential manifolds, Academic Press, 1993

[7] Y. B. Rudyak, On Thom spectra, orientability and cobordism, Springer monographs in mathematics

[8] R. M. Switzer, Algebraic topology - homotopy and homology, Springer, 1975 ICMC - Universidade de Sa˜o Paulo, Avenida Trabalhador sa˜o-carlense 400, 13566- 590 - Sa˜o Carlos - SP, Brasil E-mail address: ferrariruffino@gmail.com

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