Geometry & Topology

$\mathrm{Spin}^c$–structures and homotopy equivalences

Robert E Gompf

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Abstract

We show that a homotopy equivalence between manifolds induces a correspondence between their spinc–structures, even in the presence of 2–torsion. This is proved by generalizing spinc–structures to Poincaré complexes. A procedure is given for explicitly computing the correspondence under reasonable hypotheses.

Article information

Source
Geom. Topol., Volume 1, Number 1 (1997), 41-50.

Dates
Received: 16 May 1997
Accepted: 17 October 1997
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513882844

Digital Object Identifier
doi:10.2140/gt.1997.1.41

Mathematical Reviews number (MathSciNet)
MR1475553

Zentralblatt MATH identifier
0886.57021

Subjects
Primary: 57N13: Topology of $E^4$ , $4$-manifolds [See also 14Jxx, 32Jxx] 57R15: Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
Secondary: 57P10: Poincaré duality spaces 57R19: Algebraic topology on manifolds

Keywords
4–manifold Seiberg–Witten invariant Poincaré complex

Citation

Gompf, Robert E. $\mathrm{Spin}^c$–structures and homotopy equivalences. Geom. Topol. 1 (1997), no. 1, 41--50. doi:10.2140/gt.1997.1.41. https://projecteuclid.org/euclid.gt/1513882844


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