acase@tulane.edu

acase@tulane.edu

A recently discovered fossiliferous zone, the Chapelville fossiliferous horizon, in the Tupelo Tongue of the Coffee Sand in northern Lee County, Mississippi, contains the best preserved and most diverse molluscan fauna known from the Campanian Stage (Late Cretaceous). This fauna contains about three hundred molluscan species and is comparable in both preservation and diversity to the well known Maastrichtian fauna of the Coon Creek Tongue of the Ripley Formation at Coon Creek in McNairy County, Tennessee. Twenty-two families, forty genera, and fifty-seven species of streptoneuran gastropods (exclusive of the Stenoglossa, Ptenoglossa, and Heterostropha) are recognized and are illustrated in a series of 22 plates. Five species of archaeogastropods are described; two of which are new. The Caenogastropoda, exclusive of the Strenoglossa, Ptenoglossa, and Heterostropha, include fifty-two species; twenty-five (including one subspecies) of which are new Protoconchs of several taxa are described here for the first time. Two genera, Demasia and Lemniscolittorina, which had previously been assigned to the archaeogastropoda Family Neritidae and the caenogastropod Family Littorinidae, respectively, are reassigned to the heterostroph families Amathinidae and Mathilildae based on their protoconchs The systematic section contains a new classification that incorporates parts of the recently proposed gastropod classifications of Ponder and Waren (1988) and Haszprunar (1988a, b). The Chapelville gastropoda fauna of the Tupelo Tongue provides a window into the pre-Maastrichtian streptoneuran diversity of the northern U.S. Gulf region. It contains the earliest geologic record of many Cenozoic taxa and is surprisingly modern in many respects / acase@tulane.edu

acase@tulane.edu

acase@tulane.edu

acase@tulane.edu

The application of Seiberg-Witten theory to the study of smooth 4-manifolds over the last three years has proved extremely fruitful. In particular, progress has been made concerning the '11/8s' conjecture and the minimal genus problem. In this dissertation, we extend a '10/8s' result of Furuta to a special group of spin 4-orbifolds. This result yields information concerning the minimal genus problem of representing homology classes of a smooth 4-manifold by embedded surfaces / acase@tulane.edu

acase@tulane.edu

This dissertation is devoted to studying the following question: Let M1 and M2 be two nonhomeomorphic lens spaces, either linear or fake. When are M 1 and M2 stably homeomorphic, i.e., when is M1 x Rn homeomorphic to M2 x Rn for some n ≥ 0? We show that for fake lens spaces of dimension ≥ 5, given a tangential homotopy equivalence f : M1 → M2 the existence of an h-cobordism (W; M1, M2) is a necessary and sufficient condition for the existence of a homeomorphism between M1 x R1 and M2 x R1 . We also show that a proper h-cobordism (W; M1 x R1 , M2 x R1 ) is a necessary and sufficient condition for the existence of a homeomorphism between M1 x R2 and M2 x R2 . We also obtain an estimate of the cardinality of the set of fake lens spaces M2 which can appear in the h-cobordism (W; M1 x R1 , M2 x R1 ) For linear lens spaces of dimension ≥ 5 having fundamental group of order 2k, the existence of a tangential homotopy equivalence f : M1 → M2 implies M1 x R3 ≈ M2 x R3 . There is a long Sullivan-Wall type exact sequence &ldots;→Lhn +4&parl0;M2xR3 &parr0;→ShTOP &parl0;M2x R3&parr0;→&sqbl0;M 2xR3; G/TOP&sqbr0;→Lh n+3&parl0;M2x R3&parr0;→&cdots; relating surgery groups to the existence of a homeomorphism between M1 x R3 and M2 x R3 It turns out that in this case the surgery groups are trivial. As a consequence, the triviality of the normal invariant eta(f) ∈ [ M2; G/TOP] will show that f x id : M1 x R3 → M2 x R3 represents a trivial element in ShTOP&parl0; M2xR3 &parr0; . This when combined with some additional work leads to the conclusion that g = f x id : M1 x R3 → M2 x R3 is indeed properly homotopic to a homeomorphism Finally we apply these results to the stabilization of fake projective spaces, defined as the particular type of fake lens spaces which are quotients of 2n - 1-spheres by the action of Z2 . We prove that there are countably many nonhomeomorphic fake projective spaces, and that stabilization by multiplication with R3 is always possible / acase@tulane.edu

Stable classification of homotopy equivalences between two manifolds deals with the following question: If $f : M \to N$ is a homotopy equivalence between two manifolds, when is $f \times id\sb{\IR\sp{k}} : M \times \IR\sp{k} \to N \times \IR\sp{k}$ homotopic to a homeomorphism? Due to Mazur's result, we know that this is true as long as $k \ge\ {\rm dim} M + 2$ and f is tangential. Therefore, we try to minimize the value of k by imposing additional conditions. It is already known that if for each Sylow subgroup H of $\pi\sb1 M,$ where $\pi\sb1 M$ is finite, and the liftings $f\sb{H} : M\sb{H}\to N\sb{H}$ are homotopic to a homeomorphism, then $f\times id\sb{\IR\sp3} : M\times \IR\sp3 \to N \times \IR\sp3$ is homotopic to a homeomorphism. The next step would be to ask if under some additional conditions it is possible to obtain stabilization of f on multiplication by $\IR\sp2$. This turns out to be the most intricate case and this dissertation is devoted to its analysis The central ideas for the proof come from the inductive detection phenomenon and surgery theory of compact and non-compact manifolds. Heavy use of computational results for L-groups of cyclic groups of order $p,\ \doubz\sb{p},$ as well as analysis of the surgery exact sequence are required at several stages / acase@tulane.edu