Cross-cap

In mathematics, a cross-cap is a two-dimensional surface that is topologically equivalent to a Möbius strip. The term 'cross-cap', however, often implies that the surface has been deformed so that its boundary is an ordinary circle. This cannot be done in three dimensions, without the surface intersecting itself.

A cross-cap that has been closed up by gluing a disc to its boundary is called a real projective plane. Two cross-caps glued together at their boundaries form a Klein bottle. An important theorem of topology, the classification theorem for surfaces, states that all two-dimensional nonorientable manifolds are spheres with some number of 'handles' and at most two cross-caps.



In the News

A Powerful New Tool For Decoding Gene Functions In Mammals And Man
A collaborative project between American and Chinese researchers developed a way to study the function of genes in mice and man by using a moveable genetic element from moths, according to a report in the journal Cell. The technique should be particularly useful for identifying genes and drug targets for diseases such as cancers and diabetes.

Northwestern's Cancer Genetics Program ID's Gene Variant That Increase
A paper published in this week's Journal of Clinical Oncologysays Transforming Growth Factor Beta Receptor 1*6A (TGFBR1*6A) -- a mutated gene present in nearly one in eight people and the most commonly inherited cancer susceptibility gene identified so far -- might be responsible for a significant proportion of familial colorectal cancers.

Vote: Best Games of 2006
Gears of War? Zelda? Make sure we consider your favorite for our end-of-year video game awards. The votes are rolling in, so nominate the one that stands above the rest in your world. In Game|Life.

Immunosuppression Transplant Drug Shown To Inhibit Angiogenesis In Can
Scientists have long known that the blood vessels of tumors differ markedly from normal blood vessels. Now, a research team led by scientists at Beth Israel Deaconess Medical Center (BIDMC) has identified a signaling pathway which, when activated, transforms otherwise healthy blood vessels into the leaky, misshapen vasculature that characterizes cancerous tumors.

Keeping Cancer At Bay: Long-term Therapy In The Fight Against Multiple
There is no known cure for multiple myeloma, so its diagnosis means high-dose chemotherapy followed by repeated treatments with each relapse of the cancer -- a watch and wait approach. A new approach of providing patients with continuous therapy to keep the cancer at bay was explored by a team of international researchers from France, Switzerland and Belgium. Their findings will be published in the Nov. 15, 2006, issue of Blood.

Adult Stem Cells Lack Key Pluripotency Regulator
The protein Oct4, which helps to maintain embryonic stem cells, has been shown to be virtually absent in adult stem cells. These results question the findings of more than 50 studies that found Oct4 in various adult stem cells, and put claims of pluripotent adult stem cells into perspective.

[Funny] A referee has sent himself off in an English amateur league ma
Andy Wain had to abandon the Sunday league match between Peterborough North End and a Royal Mail side in the 63rd minute after throwing down his whistle and marching up to confront North End's keeper.

Messenger: Mercury Surface, Space Environment, Geochemistry, and Rangi
Information about the "NASA Discovery mission to conduct this orbital study of the innermost planet."Messenger launched in August 2004. It should be "in position to enter Mercury orbit in March 2011."The site provides a FAQ, an overview of the mission, status reports, facts about the planet Mercury, information for students and teachers, related links, and more. From John Hopkins University Applied Physics Laboratory (JHU/APL).

Libraries and Hurricane Katrina
Collection of resources for libraries and librarians related to the aftermath of Hurricane Katrina. Includes a link to ongoing news coverage, and links to resources for financial donations, book donations, housing, employment, and disaster recovery and preservation. Also includes links to reading resources to help victims cope and to sites with general relief information. From the American Library Association (ALA).

The Secret World of Lonelygirl
How a 19-year-old actress and a few struggling web filmmakers took on TV. A Wired magazine exclusive by Joshua Davis.


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