Helicity is a topological invariant of massless particles: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>C</mml:mi><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mn>2</mml:mn><mml:mi>h</mml:mi></mml:mrow></mml:math>

There is an elementary but indispensable relationship between the topology and geometry of massive particles. The geometric spin <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>s</a:mi></a:math> is related to the topological dimension of the internal space <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>V</b:mi></b:math> by <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mo form="prefix">dim</c:mo><c:mi>V</c:mi><c:mo>=</c:mo><c:mn>2</c:mn><c:mi>s</c:mi><c:mo>+</c:mo><c:mn>1</c:mn></c:mrow></c:math>. This breaks down for massless particles, which are geometrically characterized by their helicity <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>h</e:mi></e:math>, but all have 1D internal spaces. We show that a subtler relation exists between the topology and geometry of massless particles. Wave functions of massless particles are sections of nontrivial line bundles over the light cone whose topology is completely characterized by their first Chern number <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mi>C</f:mi></f:math>. We prove that in general <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi>C</g:mi><g:mo>=</g:mo><g:mo>−</g:mo><g:mn>2</g:mn><g:mi>h</g:mi></g:mrow></g:math>. In doing so, we also exhibit a method of generating all massless bundle representations via an Abelian group structure of massless particles.