Geometry & Topology

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

Robert E Gompf

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

4–manifold Seiberg–Witten invariant Poincaré complex


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.

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