/Users/josh/Documents
$ make
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include kk.cpp -o kk.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include planar_diagram.cpp -o planar_diagram.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include dt_code.cpp -o dt_code.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include knot_diagram.cpp -o knot_diagram.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include cube.cpp -o cube.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include steenrod_square.cpp -o steenrod_square.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include spanning_tree_complex.cpp -o spanning_tree_complex.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include smoothing.cpp -o smoothing.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include cobordism.cpp -o cobordism.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include knot_tables.cpp -o knot_tables.o
knot_tables.cpp:4:9: warning: 'HOME' macro redefined
#define HOME "/Users/josh/Documents/code/knotkit/"
^
<command line>:1:9: note: previous definition is here
#define HOME "/opt/knotkit"
^
1 warning generated.
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include sseq.cpp -o sseq.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include knot_parser/knot_parser.cc -o knot_parser/knot_parser.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include knot_parser/knot_scanner.cc -o knot_parser/knot_scanner.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include rd_parser/rd_parser.cc -o rd_parser/rd_parser.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include rd_parser/rd_scanner.cc -o rd_parser/rd_scanner.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include algebra/algebra.cpp -o algebra/algebra.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include algebra/grading.cpp -o algebra/grading.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include algebra/polynomial.cpp -o algebra/polynomial.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include lib/refcount.cpp -o lib/refcount.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include lib/lib.cpp -o lib/lib.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include lib/smallbitset.cpp -o lib/smallbitset.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include lib/bitset.cpp -o lib/bitset.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include lib/setcommon.cpp -o lib/setcommon.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include lib/io.cpp -o lib/io.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -c -O2 -g -DHOME="\"`pwd`\"" -Wall -Wno-unused -I. -I/opt/local/include lib/directed_multigraph.cpp -o lib/directed_multigraph.o
clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -L/opt/local/lib -o kk kk.o planar_diagram.o dt_code.o knot_diagram.o cube.o steenrod_square.o spanning_tree_complex.o smoothing.o cobordism.o knot_tables.o sseq.o knot_parser/knot_parser.o knot_parser/knot_scanner.o rd_parser/rd_parser.o rd_parser/rd_scanner.o algebra/algebra.o algebra/grading.o algebra/polynomial.o lib/refcount.o lib/lib.o lib/smallbitset.o lib/bitset.o lib/setcommon.o lib/io.o lib/directed_multigraph.o -lgmp -lz
clang: warning: argument unused during compilation: '-std=c++11'
/usr/bin/ld: cannot find -lc++
clang: error: linker command failed with exit code 1 (use -v to see invocation)
make: *** [kk] Error 1
If I read your issue title correctly, you are assuming that the build failure is the result of HOME pointing to the nonexistent directory /Users/josh/Documents/code/knotkit/.
However, the actual error line is /usr/bin/ld: cannot find -lc++, that is, libc++ is not installed on your machine. Most likely, this means that you are building on a Linux system (where the C++ standard library is traditionally libstdc++, not libc++) which does not provide that library.
You might be able to fix this by changing --stdlib=libc++ to --stdlib=libstdc++ in the Makefile, or by installing libc++ (e.g. via sudo apt-get install libc++-dev on Ubuntu).
I was going to say exactly what @addaleax did. @isomorphisms, did installing libc++ fix you problem? If so, I'd like to close the issue.