In [GH09] M. Goresky and N. Hingston described and investigated various properties of a product on the cohomology of the free loop space of a closed, oriented manifold M relative to the constant loops. In this thesis we will give Morse and Floer theoretic descriptions of the product. There is a theorem due to J. Jones in [JJ87] which describes an isomorphism between cohomology of the free loop space and Hochschild homology of the singular cochain algebra of M with rational coefficients. We will use the theorem of J. Jones to find an algebraic model for the Goresky-Hingston product. We then use the algebraic model to explore further properties and applications of the Goresky Hingston product. In particular we use it to compute the ring structure for the n-spheres.

The presented work investigates various theories about the significance of felid coat patterns. Most of the hypotheses are based on the theory of adaptive function of animal colouration. As regards felids, it is generally believed that the coat pattern has the function of aggressive resemblance. Early testimonies about cryptic properties of colouration of cats are summarized to provide the historical perspective of the problem. Other putative adaptive functions of patterns are investigated (intraspecific communication, thermoregulation) and close attention is paid to the option that the spotted coat of the leopard (Panthera pardus) serves as a cue for recognition from the perspective of prey. In the next stage, some of the hypotheses are tested by statistical means. The problem is simplified into search for association between a given category of a coat pattern (e.g. spots, stripes) and usual habitat of felid species (e.g. forest, grassland). Pagel's test for correlated changes is employed to account for phylogenetic relationships. In addition to broadly acknowledged hypotheses, the validity of proposition that juvenile coat patterns have the function of protective resemblance is tested. Finally, the problem of colouration of felids is linked to broader context of theoretical biology. Apart from prevailing...

In [GH09] M. Goresky and N. Hingston described and investigated various properties of a product on the cohomology of the free loop space of a closed, oriented manifold M relative to the constant loops. In this thesis we will give Morse and Floer theoretic descriptions of the product. There is a theorem due to J. Jones in [JJ87] which describes an isomorphism between cohomology of the free loop space and Hochschild homology of the singular cochain algebra of M with rational coefficients. We will use the theorem of J. Jones to find an algebraic model for the Goresky-Hingston product. We then use the algebraic model to explore further properties and applications of the Goresky Hingston product. In particular we use it to compute the ring structure for the n-spheres.