Combinatorics of embeddings

We offer the following explanation of the statement of the Kuratowski graph planarity criterion and of 6/7 of the statement of the Robertson-Seymour-Thomas intrinsic linking criterion. Let us call a cell complex 'dichotomial' if to every cell there corresponds a unique cell with the complementary set of vertices. Then every dichotomial cell complex is PL homeomorphic to a sphere; there exist precisely two 3-dimensional dichotomial cell complexes, and their 1-skeleta are K_5 and K_{3,3}; and precisely six 4-dimensional ones, and their 1-skeleta all but one graphs of the Petersen family. In higher dimensions n>2, we observe that in order to characterize those compact n-polyhedra that embed in S^{2n} in terms of finitely many "prohibited minors", it suffices to establish finiteness of the list of all (n-1)-connected n-dimensional finite cell complexes that do not embed in S^{2n} yet all their proper subcomplexes and proper cell-like combinatorial quotients embed there. Our main result is that this list contains the n-skeleta of (2n+1)-dimensional dichotomial cell complexes. The 2-skeleta of 5-dimensional dichotomial cell complexes include (apart from the three joins of the i-skeleta of (2i+2)-simplices) at least ten non-simplicial complexes.Comment: 49 pages, 1 figure. Minor improvements in v2 (subsection 4.C on transforms of dichotomial spheres reworked to include more details; subsection 2.D "Algorithmic issues" added, etc

6.2 Phenomenology

Pavel Rudolf, M. Serres / G. James, J.R. Columbo, Jean-Claude Gagnon, Richard Kostelanetz, Marguerite Dehler, Robert Morgan, W.M. Sutherland, Brian Henderson, Opal L. Nations, George Swede, M. helen J. orr, Melody Sumner, Fredo Ojda, Don Webb, Kirk Wirsig, Alexandre Amprimoz, Miriam Jones, David McFadden, Ian Kent, Ulrich Tarlatt, Fortner Anderson, Stephanie Dickinson, Marty Gervais, Yves Troendle, Richard Gessner, John Riddell, Robert Zenick, jIM fRANCIS, Richard Purdy, Stephen Bett, David Memmott, Alain-Arthur Painchaud, Beth Jankola, Denis Vanier, Josee Yvon, Huguette Turcotte, Douglas Rothschild, Lisa Teasley, Steve Reinke, Donald Brackett, Misha, Michelle LeBoutillier, Maggie Helwig, Thomas Parkinson, Karen Petersen, John Grube, B. Bali / W. Keeler, Jason Weiss, K. Shiraishi / S. Ito, David UU, Steve Venright, Bill Reid, Susan Parker, John Bennett, Margaret Christakos, Daniel Guimond, George Myers Jr., Charles Bernstein, Judy Radul, Angus Brown, Scott Moodie, P.J. Holdstock, Christian Damian, Deborah Godin, Corneil Van der Spek, M. Kettner, Giles Slade, M. A. C. Farrant, Glen Downie, Robert Kenter, G. Gilbert / S. Parker, Samuel Danzig. Cover Art: Douglas Clark

Exile Vol. XXXI No. 1

Drawing by Chris Bradley 1 How Goes the Wombat, Prithee by Jennie Benford 3 Holy Shit (for Mary) by Stephanie Athey 4-5 ..... blues by Britton R. Creelman 6 Photograph (anonymous) 7 Prose by Leigh Walton 9-12 San Jacinto by Petersen S. Thomas 13 Rebuttal by Betsy Oster 15 Running Alone by Ann Townsend McMullen 16 Windows in Florence by Michael Parr 17 Rangers by Caroline Palmer 19 Salamapo by Mary Deborah Clark 20-21 Funeral by J. K. Rand 22 Deeds Give No Title by Douglas Jones 23 Be Careful, There\u27s a Straight Bar Next Door by Karen J. Hall 25 The Rivers of Saigon by Alex Dickson 26 2 Sketches by Alfred Sturla Bodvarsson 27 Upon the Occasion of Reading 236 sonnets at One Sitting by Jeff Masten 28 I just believe in Me by Rob Jackson 29 Close by Stephanie Athey 31 Teller by Katherine Fox Reynolds 32 Woman in Greece by Michael Parr 33 Part of the Job by Joan DeWitt 35-44 Contributor Notes 46 Editorial decision is shared equally among the seven member editorial board. -title page Polymorphous: Cover Lithograph by Aimee Creelman - title pag